ORCHARD PARK - When the Buffalo Bills and Miami Dolphins take the field at Highmark Stadium Sunday afternoon, it will be the fifth time these long-time AFC East rivals have met in the postseason.

This will tie Miami with Kansas City as Buffalo’s most frequent playoff opponent since the franchise was born in 1960. Buffalo will become Miami’s most frequent opponent since it was born in 1966.

All four of the previous Bills-Dolphins games were played in the 1990s at a time when their rivalry was among the best in the NFL, and every one of the games was fascinating in its own way with Buffalo winning three.

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Since the dawn of the 21st century, the Bills-Dolphins rivalry has been mostly irrelevant because the teams have almost never been good at the same time. In fact, this is the first time since 1999 that the Bills and Dolphins have qualified for the postseason in the same year.

Here is a look back at the previous four playoff games between the teams:

Jan. 12, 1991: Bills 44, Dolphins 34

A classic first foray as the Jim Kelly and Dan Marino offenses combined for 923 yards and put up 78 points, making this, at the time, the highest-scoring non-overtime playoff game in NFL history.

And while all of this was taking place on a snowy day at Rich Stadium, the country was on edge because President George H. Bush had made it clear that war in the Persian Gulf was imminent. In fact, as several Bills came to the lectern in the interview room following the game, the television was tuned not to the NFL, but the dire situation that was only days away from unfolding half a world away.

“You just pray nothing happens over there,” Kelly said. “All we can do, though, is go about our business at home.” And the business at hand was disposing of the Dolphins.

Kelly, who returned to action after missing the final two-plus games of the regular season with a knee injury, threw for 339 yards, 271 of that plus all three of his TD passes split between Andre Reed and James Lofton. Thurman Thomas chipped in with 117 yards rushing, and the defense, despite giving up 323 yards to Marino, intercepted two of his passes, each of which set up a Scott Norwood field goal.

Buffalo had been using the no-huddle offense more and more late in the season until Kelly got hurt. But for this game, Kelly implored Marv Levy to let him run it, and Levy gave his blessing. “We had planned to start with the no-huddle offense and, as long as we had so much success with it, we stayed with it,” Levy said.

The Bills raced out to a 20-3 lead 18 minutes into the game, but 55 seconds into the fourth quarter, Marino threw a TD pass to offensive lineman Roy Foster and Miami was within 30-27. Duly woke, the Bills answered with Thomas’ five-yard TD run, and 36 seconds later, after Miami fumbled the kickoff, Kelly hit Reed with a 26-yard TD pass and it was over.

“We went with what we thought we could do best,” Kelly said of running the no-huddle. “The key to our offense is mixing it up. With all the weapons I have on offense, you can do things like that.”

Jan. 17, 1993: Bills 29, Dolphins 10

The Bills saw their four-year stranglehold on the AFC East come to an end in 1992 as they finished with the same 11-5 record as Miami, but lost the tiebreaker. Kelly had been injured in a season finale lost at Houston which cost the Bills the division, and Frank Reich took control and led the Bills to a pair of victories — the historic comeback game against those same Oilers, and then a thrashing of the Steelers in Pittsburgh.

Kelly returned for the AFC Championship Game in Miami, though some fans openly questioned whether Levy should stick with the red-hot Reich. Even Reich chuckled at that one.

Kelly didn’t have a great day as he threw for only 177 yards, but he didn’t need to be great. Thomas and Kenneth Davis keyed a 182-yard rushing effort for Buffalo, Steve Christie kicked five field goals, and the defense sacked Marino four times and forced four of Miami’s five turnovers in a dominant victory that left no doubt which team was superior.

“We knew we were the top team in the AFC,” linebacker Shane Conlan said after the Bills tied an NFL record by qualifying for a third straight Super Bowl. “We had some bad luck and lost some games, but talent-wise, we knew we had a great team.”

Kelly’s TD pass to Thomas helped stake the Bills to a 13-3 halftime lead and when Miami fumbled the second-half kickoff, Davis scored on a two-yard run less than two minutes into the third for a 20-3 lead and Miami never even came close to getting back into the game as the crowd at Joe Robbie Stadium sat there in sun-baked silence.

“We’ve made history twice in a couple of weeks, but we want to make history in two weeks by winning the Super Bowl,” said linebacker Cornelius Bennett. “If we can do that, I’ll have something to tell the kids when I get old.”

Unfortunately, the Bills made a different kind of history when they lost their third straight Super Bowl.

Dec. 30, 1995: Bills 37, Dolphins 22

The Bills made it 3-for-3 all-time against the Dolphins in the postseason, and they made more history on a cold, windy day when the wind-chill was 11 degrees. The Bills maimed Miami’s defense by rushing for 341 yards, the second-highest total ever recorded in a playoff game, most in the AFC.

Thomas led the way with 158 yards and had another 42 receiving for an even 200 yards from scrimmage. Darick Holmes added 87 yards and Tim Tindale, the Canadian Comet, gave the Bills a 34-7 lead early in the fourth when he broke a memorable 44-yard TD run up the gut to cap a career-best 67-yard output.

All of that rendered a huge day by Marino — 33 of 64 for 422 yards — rather meaningless. Not that he wasn’t responsible for some of Miami’s woes as he threw three interceptions and lost a fumble on an aborted snap.

“What they might do strategically should give you problems for about a quarter,” said Miami defensive end Jeff Cross of the Bills rather simple run game approach. “You should have it figured out and start to execute what it is we have to do better. We’ve got a lot to be ashamed of.”

They sure did. Kelly did little — 12 of 22 for 195 yards with a TD and two picks —but it didn’t even matter because the Dolphins were so thoroughly trampled on the ground.

“It’s a great feeling,” said Bills guard Jerry Ostroski. “We (the line) were looked upon as maybe a negative on this football team and it was hard for us in the beginning. We had to swallow a lot and take a lot of hits, but it just took time for us to jell. The veterans were patient, everybody was patient for us. We decided that we had to win the game for us. We blocked our butts off, played hard. Thurman ran hard, Darick made some unbelievable runs, Tim Tindale. It was just a group effort.”

Jan. 2 ,1999: Dolphins 24, Bills 17

Even in losing for the first time to Miami in the postseason, the Bills made history as wide receiver Eric Moulds set the still standing NFL record for receiving yards in a playoff game with 240, even though it wound up going for naught.

This was a fabulous game that came down to the final nine seconds when, on a first-and-goal from the 5, Doug Flutie was sacked by Dolphins defensive tackle Trace Armstrong and fumbled the ball away, one of four lost Buffalo fumbles after a regular season in which they lost a franchise-record low six.

It ended a magical year for Flutie as he returned to the NFL after being exiled in Canada for nearly a decade, then wrested the Bills QB job from Rob Johnson and led Buffalo to an 11-5 record. He threw for 360 yards in the game with Moulds catching nine including a 32-yard TD, but the giveaway at the end spoiled his storybook performance.

“I thought I was going to have a slant route and it wasn’t there,” explained Flutie. “I held on to it and turned to look over the middle and was just going to throw it over Jay Riemersma’s head out of the end zone and as I recoiled, I got hit. It’s a three-step drop, it’s not a great protection, and the ball should have been out earlier.”

On the first play of the game Moulds caught a 65-yard pass but fumbled it away at the Miami 29, and Marino turned around and drove the Dolphins to a go-ahead field goal. Miami took a 6-0 lead early in the second, then tried a surprise onside kick, but Buffalo recovered and almost immediately, Flutie hit Moulds for 37 yards to set up Thomas’ short TD run.

The teams traded third-quarter TDs before Miami opened a 24-14 lead early in the fourth to set up a frenetic finish. First, Andre Reed thought he scored on a 15-yard pass from Flutie, but after he was ruled short, he angrily got up to argue and bumped an official. That resulted in a 15-yard penalty and an ejection which proved costly as it forced the Bills to eventually settle for a Christie field goal with 1:33 left.

“It’s frustrating when you get a touchdown called back, and they give you a 15-yard penalty and you have to go for a field goal instead of getting seven points,” said coach Wade Phillips. “That game looks a lot different at the end with Andre in the game and us only three points behind.”

The Bills’ Kurt Schulz then recovered the onside kick at the Bills 31, Flutie hit Moulds for 30, and eventually they reached the 5. Had they needed only a field goal to force overtime, maybe the play call would have been different. Instead, Flutie turned it over, and the Bills season came to an end.

Sal Maiorana can be reached at maiorana@gannett.com. Follow him on Twitter @salmaiorana.To subscribe to Sal's new twice-a-week newsletter, Bills Blast, please follow this link: https://profile.democratandchronicle.com/newsletters/bills-blast

This article originally appeared on Rochester Democrat and Chronicle: Bills-Dolphins playoff history: Postseason rivalry reignites