If this was Arsene Wenger’s final time facing Jose Mourinho, as it very well might have been, he at least ended one of the game’s biggest managerial rivalries with the last laugh. Sort of.

In their 13th matchup, Wenger improved his record to a win, seven ties and five losses. At length, he had beaten the mouthy Portuguese, who had, for well over a decade, made a sport of antagonizing the studious Frenchman. And again and again, the younger Mourinho had gotten the better of the 67-year-old, who is in his 22nd and possibly final year at Arsenal.

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Thanks to goals from Granit Xhaka and Danny Welbeck, the Gunners vanquished Manchester United 2-0 in their final meeting of a mutually frustrating season. And as such, sixth-place Arsenal gained on the fifth-place Red Devils, closing the gap to two points while the Londoners have a game in hand. They both hope, of course, to wrest the fourth spot and its precious Champions League place from Manchester City – four points ahead of United – or third-place Liverpool, one point further up the table.

Then again, Man United is still eyeing the Europa League title, which also offers up a Champions League berth.

That these mighty clubs have been relegated to this sort of desperate math, hoping to claw something useful out of a lost season, is telling enough of the current state of Mourinho’s and Wenger’s laureled careers. The saving grace for Mourinho, perhaps, is that he’s only in his first year at the club and that it was all a shambles long before he arrived. But Wenger has an expiring contract and all-time low support from the fans who trusted him for decades.

In that sense, it may prove a Pyrrhic victory – good for Wenger’s endlessly battered ego, but ultimately of little use if it doesn’t produce a Champions League place or indeed save the manager’s job. Wenger will likely take it either way, such has been his obvious dislike of Mourinho, first in two spells with Chelsea and now with United.

Like many of the bouts between big clubs in the Premier League this season, this clash was fairly disappointing. An uneventful first half was followed by a tepid second one.

There was just not very much of note that happened. United had only two looks in the opening act and really none in the second. Both of those chances were instigated by Wayne Rooney. Once, he set up Anthony Martial, who was denied by Peter Cech. And the other time, he intercepted a disastrous back pass across the box from Rob Holding, but the veteran goalkeeper was wise to it again.

Arsenal, meanwhile, relied heavily on Alexis Sanchez. As usual. Early on, he played a splendid through ball for Aaron Ramsey that was parried by David De Gea. Later, the Chilean’s cutback was cleared and Alex Oxlade-Chamberlain’s deflected shot was read well by De Gea.

Not 10 minutes after halftime, Xhaka’s long shot took an enormous deflection off Ander Herrera’s back and dropped into the net behind him. And just three minutes later, Oxlade-Chamberlain swung in a big, looping cross for the wide-open Welbeck, who came up at United but was never given a real chance. Welbeck’s header caromed in off the underside of the bar for a 2-0 Gunners advantage.

It was the rare occasion when Mourinho was punished for his unadventurous approach – to put it charitably – in a big game. Certainly, a tie would have suited him better, likely killing off Arsenal’s challenge. Mourinho closed up shop in spite of all that technical ability in the team, not to mention his thin back line, in which he rested several players and handed a full debut to teenager Axel Tuanzebe. He went down with his tactics.

After the final whistle, the managers coolly shook hands and slipped into the tunnel. At last, Wenger had prevailed. At the very least, he has accomplished that this year.

Leander Schaerlaeckens is a soccer columnist for Yahoo Sports. Following him on Twitter @LeanderAlphabet.

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