Chelsea went top of the English Premier League with a 1-0 victory at Birmingham City, while Manchester United got back to winning ways by beating promoted Norwich City 2-1 on Saturday.
Chelsea, who started the season by beating United 1-0 last weekend, had been struggling to break Birmingham down before substitute midfielder Joe Cole scored with a deflected shot.
Frenchman David Bellion and new striker Alan Smith, volleying a superb first league goal, set United on their way at Old Trafford before substitute Paul McVeigh pulled one back for Norwich to set up a tense finale.
Captain Steven Gerrard fired Liverpool to a 2-1 comeback victory over Manchester City, Newcastle United suffered their first home defeat of 2004 when they went down 1-0 to Tottenham Hotspur and 10-man Everton won 3-1 at Crystal Palace.
Fulham made a winning return to Craven Cottage, beating Bolton Wanderers 2-0 with both goals from Andy Cole, and striker James Beattie converted a stoppage-time penalty to give Southampton a dramatic 3-2 win over Blackburn Rovers.
Champions Arsenal are at home to Middlesbrough on Sunday, hoping to equal Nottingham Forest's 42-game unbeaten run in the English top flight.
As in last weekend's win over the FA Cup holders, Chelsea lacked sparkle but got the result Mourinho wanted.
Cole's 68th minute strike signalled an ideal return from injury, having been ruled out of the win over United and England's midweek friendly victory over Ukraine.
Though big-spending Chelsea had to battle hard for the points, Mourinho told Sky Sports News: "I wasn't expecting any different...I knew what was waiting for us.
MOON PLAYERS
"People still speak about money, stars and players coming from the moon, but I can tell you it's very difficult to have top players fighting like my players are fighting. Normally, top players are not ready to fight so much."
Liverpool made heavy weather of their win, with French striker Nicolas Anelka giving City a first-half lead against his old club.
Czech forward Milan Baros, top scorer at Euro 2004, got his first of the season for Liverpool just after the break and Gerrard drove home the second with 15 minutes left, shortly before a red card for City defender Richard Dunne.
Liverpool's new Spanish coach Rafael Benitez summed up his first game at Anfield, saying: "The score is good, the team played well, the supporters enjoyed it and at the end I'm very happy."
Spurs rounded off a miserable week for Newcastle when new Cameroon signing Thimothee Atouba scored a superb solo goal on the break after Jacques Santini's side had soaked up all the pressure.
Newcastle were hit by controversy after England midfielder Kieron Dyer refused to play on the right flank in last weekend's draw at Middlesbrough and was on the verge of being transfer-listed before apologising.
Manager Bobby Robson then lost his best defender when Real Madrid made an unexpected midweek swoop for Jonathan Woodgate, who was presented at the Bernabeu earlier on Saturday.
"I took a risk in putting Dyer on because I trusted our public. They didn't let me down," said Robson after using the midfielder as a substitute.
"He was a little bit wary as to how it would go but he was full of courage, he had it in his head that he would not let them down and he didn't.
"We've lost a game we shouldn't have lost in the first half, where we were clearly the better side."
Spurs' new manager Santini, whose side drew with Liverpool last weekend, said: "For a young team who want good performances, having two good results like these are very important for confidence."
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