Chris Wood opened the scoring for Burnley in the 31st minute
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.
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 stay 18th after the defeat but the three points for Burnley take them up to 14th, 11 points clear of their opponents.
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.
Brighton are now 17th, five points clear of safety, after they were thrashed 5-0 at home by Bournemouth.
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 climb above Chelsea into third with the win.
Elsewhere, Fulham, whose relegation is also already confirmed, won for the first time since January by beating Everton 2-0 at Craven Cottage.
