Manchester City and Manchester United remain joined at the hip at the top of the Premier League, separated only by a few goals, after both secured wins on Saturday.

City cruised after a late-first-half opener against bottom-dweller Crystal Palace, while United clung to Romelu Lukaku’s first-half goal and saw out a 1-0 away win at Southampton.

Elsewhere, Alvaro Morata bagged a hat trick in a Chelsea romp at Stoke, and Oumar Niasse, no longer in exile, scored two goals off the bench to get Everton its first win since the season’s opening day.

But we’ll start our roundup with the Premier League leaders:

Leroy Sane sparks City

Crystal Palace were surprisingly resistant to City’s advances throughout the first half, and Roy Hodgson’s side had its eyes on the halftime dressing room at 0-0. But Sane broke the resistance with a dexterous bit of skill in the box:

Even at only 1-0, Palace’s hopes seemed all but dashed. And its defending reflected that. Sane had all kinds of space down the left to set up Raheem Sterling for City’s second:

And at that point, the party was in full flight. Sergio Aguero nearly got on the scoresheet by slaloming through Palace’s defense. He then squared to Sterling on the volley for City’s third, and made it 4-0 himself.

Fabian Delph made it 5-0 late on.

Anything but a City win over Palace – who still hasn’t notched a goal or a point – would have been a shock. There are no grand takeaways from a comfortable 5-0 victory.

However, Saturday put City’s embarrassment of attacking riches on display. Gabriel Jesus was rested. Sane is not typically part of Pep Guardiola’s first-choice 11. But in a team like City’s, one that is so relentlessly good all over the pitch, rotation is possible. The talent makes the system hum, and the system thus makes slight talent drop-offs palatable. And those drop-offs are only ever so slight – Sane would start regularly for at least 95 of the top 100 clubs in the world. Bernardo Silva, who came off the bench Saturday, would start would at least 90 of them. That’s the extent of City’s quality and depth.

United keeps pace

United had the far tougher fixture of the two league-leading Manchester clubs, and had the far tougher time Saturday. Southampton had more shots (14 to United’s nine) and more possession (61 percent) on the afternoon. But as has been the pattern for United in Jose Mourinho’s second season, it got its goal, blocked up any potential leaks at the back, and claimed three points.

Lukaku almost singlehandedly put United in front with brute strength and persistence. He shrugged off a Southampton center back, and scuffed home a rebound after Fraser Forster had repelled his initial header:

Mourinho went into full-on “protect what we have” mode late on. Rather than replace attackers with fresh-legged attackers to accentuate his counterattack, he supplemented his original back four with Chris Smalling and Daley Blind. The fortified team packed less punch on the counter as it had in previous games that had followed similar scripts. But in the end, it did the same job. The Red Devils continued their strong start.

Chelsea storms past Stoke

Chelsea jumped back into third place, and remained just three points behind the two Manchester clubs, with an impressive 4-0 win at Stoke.

Morata opened the scoring for the Blues inside two minutes:

Pedro doubled the lead in the first half, and Morata engineered a brilliant third in the 77th minute:

Five minutes later, he completed his hat trick:

Morata’s reception in the Premier League, both from Chelsea fans and others, has been stained by an odd skepticism. But he’s now scored six goals and tallied two assists in five starts and one substitute appearance. That’s a pretty darn good return, especially leading an attack that’s been without its best playmaker. Who cares if he’s not Diego Costa? He’s his own player, and a really effective one at that.

Everton’s unlikely hero

With 50 minutes gone at Goodison Park on Saturday, the crescendoing concern surrounding Everton was as loud as ever. The Toffees trailed lowly Bournemouth 1-0, and didn’t necessarily look like fashioning an equalizer, much less a winner.

On 55 minutes, Ronald Koeman replaced the club’s prodigal son, Wayne Rooney, with a player whom he’d previously told to leave Everton, Oumar Niasse.

On 77 minutes, Niasse became the toast of Goodison:

On 82 minutes, he became the improbable match-winner, and quieted the unrest on Merseyside, at least temporarily.

Earlier in the day …

Tottenham carved up West Ham, then held on for a 3-2 victory thanks to Harry Kane, Dele Alli, Christian Eriksen and … Andy Carroll.

Other scores

Burnley 0-0 Huddersfield
Swansea 1-2 Watford

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Henry Bushnell covers soccer – the U.S. national teams, the Premier League, and much, much more – for FC Yahoo and Yahoo Sports. Have a tip? Question? Comment? Email him at henrydbushnell@gmail.com or follow him on Twitter @HenryBushnell.