Darren Fletcher scored with a header as Manchester United achieved a victory that cut out the results crisis. But the team still has 10 points to make up on Chelsea, which last lost in the league to Manchester City a year ago.
"We didn't deserve to lose this game," said Chelsea coach Mourinho, whose team now leads second-place Wigan by six points instead of nine. "Today we showed why we are champions and why we are top of the league. I believe that there is no problem for us. I am not afraid for the future.
"In the same way I give (United) credit. I hope they can realize why Chelsea are champions, top of the league and I believe will be champions again."
Chelsea's runaway start to the season, winning the first nine games to leave its big rivals well behind, had led to dismay that the English league had lost its competitive edge. But the 67,864 fans packed into Old Trafford were on the edge of their seats from start to finish.
Ruud van Nistelrooy sent an easy chance over the bar and Wayne Rooney saw a goalbound shot beat the goalkeeper but bounce off a defender.
When Chelsea had the United defense creaking in the second half, goalkeeper Edwin van der Sar dashed off his line to block Frank Lampard's close range shot and Chelsea defender Asier del Horno volleyed over the bar while unmarked.
"It was a fantastic game, a magnificent spectacle," said United manager Alex Ferguson, whose team appeared in crisis after a 4-1 Premier League loss to Middlesbrough followed by a 1-0 Champions League defeat at French club Lille.
"For the first hour we were terrific and then, until the last five minutes, we were under the cosh. They threw everything at us and that's what champions do."
Ferguson bristled when reminded that his team appeared to be in disarray during the buildup to the game with injured team captain Roy Keane criticizing teammates for the slump.
"We once went 13 games without winning. There's always pressure here," said Ferguson, whose future after 19 years at the club appeared in doubt. "Winning is always important here. How you handle yourself and compose yourself is important. I think the players and staff have shown great dignity despite the criticism leveled at them."
Hoping to rebound from the defeat by Betis, the Blues could have been two goals up before going behind to Fletcher's header.
Didier Drogba expertly controlled a long through ball from Lampard but his hurried, angled shot was blocked by Van der Sar. Left back Del Horno was left alone at the far post when Damien Duff swung over a free kick from the right only to shoot wide of the post.
As if stung by those two close shaves, United put together two standout moves and went ahead.
Mikael Silvestre's long ball sent Rooney down the left and the 20-year-old England star pulled it back expertly for Paul Scholes. The midfielder met it first time but his shot flew just past the post with 'keeper Petr Cech beaten.
It was the prelude to a well worked goal which had a lucky finish.
Rooney won the ball on the edge of the Chelsea area and fed Scholes, who slipped it out to Cristiano Ronaldo. The Portuguese winger turned a defender and floated a cross toward Fletcher, who jumped to lob a header inside the far post.
"I believe that he didn't intend to score," Mourinho said. "He tried to play in into the central area."
Instead the ball looped over the heads of Cech and defender John Terry and inside the far post.