Chelsea needed late goals from Dutchman Arjen Robben and England's Joe Cole to earn a 2-0 win at Portsmouth and extend their lead in the Premier League to eight points on Tuesday.
However, they failed to shake off a resurgent Manchester United who later beat Aston Villa 1-0 to register their seventh win in eight league games and move up to third in the table.
Chelsea lead with 49 points, champions Arsenal have 41 before facing Newcastle United on Wednesday and United are third on 40 points. Goal difference separates Alex Ferguson's men from an Everton side who lost 2-0 at Charlton Athletic.
Middlesbrough beat Norwich City 2-0 with goals from Cameroon striker Joseph-Desire Job to stay fifth on 35 points, one ahead of Liverpool, who edged Southampton 1-0 with a winner from French forward Florent Sinama-Pongolle.
Up at the top, Robben broke the deadlock for Chelsea in the 79th minute of a tricky match at Fratton Park against a Portsmouth side beaten only once in their previous six games.
"They made it very difficult for us," Mourinho told Sky Sports News. "They're playing well, they're getting results, the players are good and the organisation is good.
"But in the second half I think we discovered the positions we had to use to break the balance in their defensive system.
"By the end of the game, I think we deserved to win...and I just told my players that it was a really big victory for us."
Robben, who was booked for pulling off his shirt to celebrate his seventh goal for Chelsea, said: "It was very stupid...but I think the manager will forgive me."
Chelsea's next opponents are Liverpool, who sealed a third consecutive league win thanks to Sinama-Pongolle's goal and another inspired performance from skipper Steven Gerrard.
As for hosting Chelsea on Saturday, he said: "We know it's a very difficult game -- they're a good team, with confidence. But we are playing at home and we can win against any team at home."
Welsh winger Ryan Giggs, Manchester United's best player on the night, scored their winner with a fine shot on the bounce shortly before the break at Villa Park.
Villa piled on the early second-half pressure but created few clear-cut chances, while United's Portuguese substitute Cristiano Ronaldo caused problems for the hosts and team mate Alan Smith missed a sitter from four metres out in the closing minutes.
Ferguson said: "It was the hardest away game of the season, a fantastic, open, end-to-end game...we showed a lot of guts tonight, good character in the team. We weren't going to lose."
As for United's progress after an erratic start to the season, Ferguson said: "We're climbing up the table...it's getting to Chelsea that's the problem.
"They're on a great run and obviously we just hope they stumble and if we can keep our consistency going, we'll go very very close."
Everton suffered their first league defeat for nearly two months in a pulsating final eight minutes at Charlton, conceding two goals and having Scottish striker Duncan Ferguson sent off.
Birmingham City won 3-2 at Fulham and Blackburn Rovers moved further away from the drop zone with a 1-0 win at struggling Bolton Wanderers, who have now lost six on the trot.
Tottenham Hotspur were denied a sixth consecutive league win by Andrew Johnson in a 1-1 draw with Crystal Palace, while an 85th-minute own goal by Manchester City defender Richard Dunne cost them a 1-1 draw with 10-man West Bromwich Albion.