Chelsea chalked up their first win since January 15, albeit with an unconvincing performance, to ease the pressure on boss Graham Potter.
Wesley Fofana’s first-ever Premier League goal, scored early in the second half – only the seventh goal Chelsea have scored in four months – ended a run of three successive defeats in all competitions for the Blues.
Potter’s side had enough chances to be out of sight in the first half, with Joao Felix hitting the bar and Kai Havertz and Ben Chilwell both squandering good scoring opportunities in the box.
Leeds offered little in attack before the break but frustrated Chelsea until seven minutes into the second half when Fofana rose unmarked to head in Chilwell’s corner.
The visitors looked more threatening after going behind as the home crowd grew nervous after the substitution of Matteo Kovacic conceded much-needed legs in midfield.
That allowed Leeds to enjoy their best spell of the match in the final 15 minutes as they pressed hard for an equaliser, with Luke Ayling heading just wide and a goalmouth scramble leading to a Tyler Adams shot that was saved by Kepa.
In the dying seconds Leeds keeper Illian Meslier, up for a corner, met the delivery with a diving header but Kepa was on hand to hold on to the ball – and the three points.
Chelsea: Arrizabalaga, Loftus-Cheek (Chalobah 84), Badiashile, Koulibaly, Fofana, Chilwell, Fernandez (Madeuke 85), Kovacic (Chukwuemeka 75), Felix (Gallagher 68), Sterling (Zakaria 68), Havertz.
Subs not used: Bettinelli, Aubameyang, Mudryk, Ziyech.