Avram Grant lost his opening match as Chelsea's coach after taking over from Jose Mourinho on Friday, with his side going down to 2-0 defeat to Manchester United at Old Trafford in the Premier League on Sunday.
Argentine Carlos Tevez scored his first goal for United when he dived in to head home a Ryan Giggs cross deep into stoppage time at the end of the first half.
Chelsea were already down to 10 men by then after referee Mike Dean's controversial decision to send off John Obi Mikel after 32 minutes for a foul on Patrice Evra.
He made another contentious decision in the 88th minute judging Tal Ben Haim to have fouled Louis Saha, who scored from the ensuing penalty.
The outcome moved United into second place on 14 points, two behind leaders Arsenal.
In Sunday's other matches, Bolton and Tottenham drew 1-1, Portsmouth beat Blackburn Rovers 1-0, Aston Villa beat Everton 2-0 and Newcastle United routed West Ham 3-1.
England striker Michael Owen was substituted for the second successive match in Newcastle United's 3-1 win over West Ham United.
Owen, who has returned to the Newcastle and England teams this season after missing most of last season because of injury, was replaced after 51 minutes by Obafemi Martins as a precaution against a niggling groin injury.
He also came off early in the second half of Newcastle's defeat at Derby County on Monday and the club are closely monitoring the situation before determining whether he needs a hernia operation.
Owen, who has scored five times for club and country this season, failed to find the net on Sunday but Newcastle won thanks to two goals from Mark Viduka and one from Charles N'Zogbia. Dean Ashton scored for West Ham.