- Conte and Mourinho's already tense relationship showed no signs of improving after the Chelsea boss ignored his United counterpart for the traditional post-match handshake between managers.
- Mourinho, twice sacked by Chelsea despite winning the English title three times, insisted he had done all he could to observe the formalities after his third successive defeat at Stamford Bridge.
Manchester City were left with a healthy eight-point lead at the top of the Premier League after second-placed Manchester United suffered a 1-0 loss away to champions Chelsea hours after the leaders saw off Arsenal 3-1 on Sunday.
United manager Jose Mourinho, a former title-winning boss with Chelsea, saw his latest visit to Stamford Bridge end in defeat courtesy of Alvaro Morata's 55th-minute header that ended a run of six games without a goal for the Spain striker.
Victory left Chelsea fourth, nine points off the summit.
It was a much-needed win for Chelsea and under-pressure manager Antonio Conte following their midweek Champions League loss away to Roma.
Conte and Mourinho's already tense relationship showed no signs of improving after the Chelsea boss ignored his United counterpart for the traditional post-match handshake between managers.
"It's not important. You have to have the respect on the pitch not outside the pitch," Conte, who at full-time raced onto the pitch to celebrate with his players said.
Mourinho, twice sacked by Chelsea despite winning the English title three times, insisted he had done all he could to observe the formalities after his third successive defeat at Stamford Bridge.
"You don't want me to chase him into the middle of the pitch," he said. "He (Conte) doesn't have to wait. There is no problem with it at all."
Turning to the result, Mourinho was in defiant mood.
"We are second - not fifth, sixth or seventh or eight," he said. "We have several teams in a more difficult position than we have."
Earlier, City were impressive against the Gunners, with Kevin De Bruyne firing Pep Guardiola's men into an early lead at the Etihad before Sergio Aguero made it 2-0 from the penalty spot early in the second half.
Alexandre Lacazette pulled a goal back for the Gunners but Gabriel Jesus put City 3-1 up in the 74th minute despite a suspicion of offside, with Arsene Wenger's Arsenal now 12 points behind City.
"The third goal, at 2-1 we are in the game and he (referee Michael Oliver) gives a clear offside goal. And, of course, that kills the game for us," said Wenger.
However, City counterpart Guardiola had no truck with suggestions his side had been fortunate to win.
"We won in the best way and we deserved by far the victory," said Guardiola after City backed up their midweek Champions League win away to Napoli.