Romelu Lukaku scored his third goal in two games as Chelsea moved to the verge of securing a Champions League spot.
Mason Mount and Christian Pulisic netted before Lukaku’s late third capped a resounding win.
Relegation-threatened Leeds played most of the game with 10 men after Daniel James was red-carded for a reckless challenge on Mateo Kovacic – who limped off as a result – midway through the first half.
Chelsea were already leading and in control at that stage, with Mount having scored after just four minutes.
A slick Blues move culminated in Reece James pulling the ball back to Mount, who brilliantly fired home from near the edge of the penalty area.
Pulisic doubled the visitors’ lead after another lovely move 10 minutes into the second half.
James was again involved, finding space on the right and playing the ball inside to Jorginho, who in turn directed it towards Mount, whose clever back-heel teed up Pulisic for an emphatic finish.
It was a frustrating night in front of goal for Lukaku before his persistence was rewarded with seven minutes remaining after Leeds’ Diego Llorente had lost possession.
Hakim Ziyech set up the Belgian striker, who changed direction and managed to score despite being surrounded by Leeds defenders.
Chelsea: Mendy, Chalobah, Christensen, Rudiger, James (Azpilicueta 78), Jorginho (Loftus-Cheek 30), Kovacic, Alonso, Mount, Lukaku, Pulisic (Ziyech 78).
Subs not used: Kepa, Silva, Werner, Barkley, Havertz, Sarr.