Cesc Fabregas scored early in the second half as Chelsea maintained their five-point lead at the top of the table with a 2-1 win away to Crystal Palace.
Sergio Agüero scored all four in a 4-1 win for Manchester City over Tottenham in the lunchtime kick-off, while Danny Welbeck netted in injury time to salvage a 2-2 draw for Arsenal at home to Hull.
José Mourinho’s leaders were pushed to the limit in a fiery London derby at Selhurst Park.
Oscar's sixth-minute free-kick put the visitors - without the injured Diego Costa - in front before Cesar Azpilicueta was issued a straight red card for a foul on Mile Jedinak five minutes before the break.
Palace's numerical advantage lasted three minutes before Ireland's Damien Delaney was dismissed for a foul on Loic Remy.
Fabregas's first Premier League goal for his new club put Mourinho's men back in front before a late strike from Fraizer Campbell left the visitors hanging on for the final whistle.
Arsene Wenger breathed a sigh of relief as Arsenal's Welbeck struck in added time to salvage a point against the Tigers.
Alexis Sanchez had given the Gunners a 13th-minute lead but Mohamed Diame hit a controversial equaliser four minutes later despite appearing to foul Mathieu Flamini in the build-up.
Despite losing goalkeeper Steve Harper to an arm injury before the break, Hull went ahead through an Abel Hernandez header and looked set to hang on for a famous win before Welbeck struck.
Diafra Sakho maintained his fine scoring form as West Ham won 3-1 at Burnley to rise to the heady heights of fourth place.
The Senegalese star made it five wins in five starts when he headed a 49th-minute opener for his side at Turf Moor.
Enner Valencia added a second for the Hammers five minutes later before Burnley rallied with George Boyd reducing the deficit and Danny Ings coming agonisingly close to an equaliser.
Carlton Cole's header in the 70th minute completed another impressive afternoon for the Hammers and gave Sam Allardyce, who turns 60 on Sunday, another cause for celebration.
In the delayed kick-off at St James's Park, Gabriel Obertan's 71st minute goal was the winner for Newastle against Leicester City.