Arsenal won 4-1 at Sunderland and Liverpool prevailed 4-2 at Crystal Palace, but City's win kept Pep Guardiola's side above them
Sergio Aguero and Ilkay Gundogan each scored twice as Manchester City crushed West Bromwich Albion 4-0 on Saturday to keep their noses in front in the Premier League.
Arsenal won 4-1 at Sunderland and Liverpool prevailed 4-2 at Crystal Palace, but City's win kept Pep Guardiola's side above them both on goal difference as they ended a six-game winless run.
"When we lose there are always doubts," said Guardiola. "It's the first time I have not won in six games. Always you have doubts, (but) not over the principles."
Jose Mourinho was sent to the stands and Ander Herrera dismissed as Manchester United drew 0-0 at home to Burnley despite having 37 shots at goal, while champions Leicester City drew 1-1 at Tottenham Hotspur.
Guardiola, whose team host his former club Barcelona in the Champions League on Tuesday, made eight changes to his starting XI from Wednesday's 1-0 League Cup defeat at Manchester United.
Aguero was among the players who returned to City's starting line-up at The Hawthorns and his first-half brace effectively settled the game.
He broke the deadlock in the 19th minute, slamming a shot between Ben Foster's legs from Gundogan's pass, and doubled his tally nine minutes later with a stunning shot from the edge of the box.
The goals ended Aguero's six-game scoring drought and lifted his City tally to 149 -- one more than club great Francis Lee.
Aguero teed up Gundogan for City's third in the 79th minute and the former Borussia Dortmund midfielder sealed victory in the last minute of normal time.
"We need Sergio," said Guardiola, who dropped the Argentina striker for City's 4-0 defeat at Barcelona. "He is one of the best."
Manchester United's title hopes faded a little after their stalemate with Burnley left them eight points off top spot in eighth place.
Former United goalkeeper Tom Heaton was Burnley's saviour, producing stunning saves from Jesse Lingard, Paul Pogba and Zlatan Ibrahimovic.
United also hit the woodwork in the second half through Juan Mata and Ibrahimovic.
Mourinho was sent to the stands at half-time, reportedly after complaining about referee Mark Clattenburg's failure to award Matteo Darmian a penalty.
Herrera was sent off in the 70th minute after being shown a second yellow card for sliding in on Dean Marney.
"I think the referee did fantastic work. I won't say more than this," United assistant Rui Faria, who faced the media instead of Mourinho, said sarcastically.
"The people in the stadium could feel that the players gave everything. We fought until the last second. We have to keep working and things will happen."
Arsenal had earlier strolled to victory at bottom club Sunderland, who are without a win after 10 league games and have made the worst start to a Premier League season.
Alexis Sanchez put Arsenal in front in the 19th minute with a header from an Alex Oxlade-Chamberlain cross.
Jermain Defoe equalised from the spot in the 65th minute after Petr Cech was booked for impeding Duncan Watmore.
But Olivier Giroud restored the visitors' advantage six minutes later, volleying in a Kieran Gibbs cross with his first touch after coming on, and he scored again with his head before Sanchez completed the scoring.
Jurgen Klopp's Liverpool joined City and Arsenal on 23 points courtesy of an entertaining victory at Palace.
Palace midfielder James McArthur hit back twice to haul the hosts level after Liverpool went ahead first through Emre Can and then Dejan Lovren.
But Joel Matip's 44th-minute header restored the visitors' advantage and Roberto Firmino chipped in from Jordan Henderson's pass to seal victory with 19 minutes remaining.
"Nice and easy game, eh!" Liverpool manager Klopp exclaimed with a smile on BT Sport.
"I don't think we've played much better offensive-wise. But then we opened the game by ourselves again.
"Close game, deserved win at the end. I'm very happy at the moment."
Tottenham were left three points off the pace in fourth place after drawing at home to Leicester, who climbed one place to 11th.
Vincent Janssen gave Spurs the lead with a 44th-minute penalty, but Ahmed Musa equalised early in the second period, sliding in bravely to apply the finishing touch to Jamie Vardy's cross.
Watford stole above United into seventh place after edging Hull City 1-0 courtesy of a late Michael Dawson own goal.
Middlesbrough pulled clear of the relegation places after beating Bournemouth 2-0 through a memorable Gaston Ramirez solo goal and a Stewart Downing strike.