A sweeping move starting in their own box took Leeds down the right flank and midfielder Pablo Hernandez pounced on a cutback to take a low shot that went in off the far post.
Leeds moved to 84 points while second-placed West Bromwich Albion, who were held to a 1-1 draw by Blackburn Rovers on Saturday, are on 81 with three games left.
Swansea, who remained in seventh place, missed the opportunity to climb into the playoff spots and sit a point behind sixth-placed Cardiff City.
Stoke City, who started the day a point above the relegation zone, beat Birmingham City 2-0 for only their second win after the restart thanks to first-half goals from Danny Batth and Samuel Clucas.
Stoke moved up from 21st to 17th in the standings -- above Birmingham on goal difference -- to give Michael O'Neill's side breathing room in the battle for survival.
Chelsea have three games to save Kai Havertz deal – Euro Papers