Patrick Bamford put the visitors ahead inside five minutes before Olivier Giroud - in the starting line-up in the league for the first time this season after his four-goal haul against Sevilla - levelled the scores.
Chelsea created most of the chances and went ahead in the 61st minute when Kurt Zouma jumped higher than everyone to power a Mason Mount corner down and into net.
Christian Pulisic sealed the win in added time when he turned in a cross by Timo Werner.
The win pushed Chelsea up to top spot in the table with 22 points, leap-frogging Tottenham and Liverpool who both have 21 and are playing on Sunday. Leeds are in 12th position.
The game marked the return of fans to Stamford Bridge for the first time since March, before the first coronavirus lockdown, giving 2,000 supporters the chance to watch several Chelsea players in the flesh for the first time after the club's summer spending spree.
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