Mourinho's Tottenham Hotspur won a 3-2 victory over West Ham United with goals from Son Heung-min, Lucas Moura and Harry Kane.
Jose Mourinho began life as Tottenham Hotspur manager with a 3-2 victory at West Ham United on Saturday, while Premier League pacesetters Liverpool won to remain eight points clear and defending champions Manchester City also took three points.
The use of VAR continued to be a major talking point, however, having a say in Liverpool's 2-1 win at Crystal Palace and second-placed Leicester City's 2-0 triumph at Brighton & Hove Albion. Manchester City fought back to beat Chelsea 2-1.
Liverpool has 37 points from 13 games, with their unbeaten Premier League run now stretching to 30 games going back to last season, with Leicester on 29, City with 28 and Chelsea 26.
Norwich City, Burnley and Wolverhampton Wanderers all won away but Southampton was denied victory by a 96th-minute Arsenal equaliser from Alexandre Lacazette in a 2-2 draw.
That result will pile more pressure on manager Unai Emery, particularly after Mourinho's winning start at rivals Spurs produced their first success on the road in 10 months.
The 56-year-old Portuguese head coach's new side should really have romped home after strikes by Son Heung-min, Lucas Moura and Harry Kane, whose 175th goal for the north London club moved him up to third on their all-time scorers' list.
Mourinho chose to highlight the contribution of midfielder Dele Alli, who produced an outrageous piece of skill in the lead-up to Spurs' second goal by somehow scooping the ball down the line to Son when it had appeared out of play.
"(Alli's) too good to not be one of the best players in the world and not playing with the national team (England)," said Mourinho, who hugged the midfielder warmly as he left the field.
But Mourinho admitted he was disappointed with the way Tottenham leaked two late goals, a familiar failing from a side who have kept one clean sheet in the league all season.
"I was really happy before we conceded the two goals, we were playing well, bringing to the game things we had tried in training," said 56-year-old Mourinho.
Spurs are ninth on 17 points with West Ham 16th on 13.
Liverpool grabbed another late winner through Roberto Firmino at Selhurst Park against a spirited Palace side who were controversially denied an opener from James Tomkins after VAR spotted a push on defender Dejan Lovren.
Juergen Klopp's team rode their luck to take the lead through Sadio Mane after the break, although Wilfried Zaha gave Palace hope of a point with a goal in the 82nd minute before Firmino intervened to make it 12 league wins out of 13.
The win put pressure on City, beaten at Anfield before the international break, to win in their top-four clash with Frank Lampard's Chelsea side.
The Londoners started brightly and grabbed a 22nd-minute lead through N'Golo Kante, who beat Ederson after latching on to a superb through ball from Mateo Kovacic.
But City struck back twice before the break with a fortunate deflected shot from Kevin De Bruyne and then a fine, solo strike from Riyad Mahrez.
The result ended a six-match winning streak for the young Chelsea side, who continue to win admirers with their lively and progressive approach.
"We went toe-to-toe," said Lampard. "The amount of time we got in their final third we didn't have that little bit of quality. Games like that can be lost in the boxes."
VAR, the season's perennial talking point, also had a say at Brighton, where Leicester's Jamie Vardy was ordered to retake his penalty as the Foxes secured a fifth straight league win after Ayoze Perez had opened the scoring for the visitors.
Arsenal has dropped further away from the Champions League qualifying places after a poor result against Southampton, with boos ringing around the Emirates stadium despite Lacazette's 96th-minute goal -- his second equaliser of the game.
"We're kicking ourselves," said Southampton's James Ward-Prowse after they failed to hold on for the win. "On a positive note, it's a building block for us and we have some winnable games coming up."
Everton's Marco Silva is another manager feeling the heat following his side's 2-0 home defeat by Norwich City, a result that moved the visitors off bottom spot.
They are replaced by Watford, who lost 3-0 to Burnley after strikers Chris Wood and Ashley Barnes scored in the second half to secure their team's first away win of the season.
Wolves moved up to fifth as Joao Moutinho and Raul Jimenez earned Nuno Espirito Santo's reinvigorated side a 2-1 win at 10-man Bournemouth, who had Simon Francis dismissed 37 minutes into his first league start since Boxing Day for a second booking.