Paul Pogba scored twice from the penalty spot as Manchester United defeated West Ham 2-1 to move above Arsenal into fifth position – two points behind the Blues, who have 66 points.
Earlier, Lucas Moura scored a hat-trick for Tottenham in the early kick-off as his side beat already relegated Huddersfield 4-0.
Victor Wanyama scored the other goal for Spurs, who climbed above Chelsea into third with the win.
Southampton beat Wolves 3-1 at St Mary’s Stadium with two goals from Nathan Redmond and one from Shane Long to move eight points ahead of Cardiff in 16th.
Burnley beat the Bluebirds with goals from Chris Wood but at 1-0 Cardiff were awarded a penalty for handball, only for referee Mike Dean to reverse his decision.
Cardiff’s relegation fears increased with a controversial 2-0 defeat by relegation rivals Burnley, while Southampton also took a big step towards safety with a win.
Cardiff stay 18th after the defeat but the three points for Burnley take them up to 14th, 11 points clear of their opponents.
Brighton are now 17th, five points clear of safety, after they were thrashed 5-0 at home by Bournemouth.
Elsewhere, Fulham, whose relegation is also already confirmed, won for the first time since January by beating Everton 2-0 at Craven Cottage.