Thomas Tuchel's side won for the first time since Todd Boehly's consortium agreed a deal to buy Chelsea from Roman Abramovich last week.
Mason Mount opened the scoring in the early stages at Elland Road and Leeds suffered another blow when Daniel James was sent off.
Christian Pulisic bagged Chelsea's second goal after half-time and Romelu Lukaku wrapped up the Blues' first win in four games.
Third-placed Chelsea are now eight points clear of fifth-placed Tottenham and will be guaranteed a top-four finish if Antonio Conte's team fail to beat fourth-placed Arsenal on Thursday.
Arresting their worrying recent slump was the ideal preparation for Chelsea ahead of Saturday's FA Cup final against Liverpool at Wembley.