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 halftime 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.
"We accepted all the obstacles we'd have to face, a physical team and an emotional stadium. We were strong from the beginning and deserved to win," said Tuchel, who revealed Mateo Kovacic could miss the final with an ankle injury.
While Chelsea look to end the season on a high, Leeds are in grave danger of relegation.
Jesse Marsch's men sit third-bottom of the table, behind fourth-bottom Burnley on goal difference.
Burnley have three games left compared to only two for Leeds, who host Brighton and travel to Brentford in the matches that will decide if their two-season stay in the top flight is destined to end with a return to the Championship.
Everton moved two points clear of Leeds after a 0-0 draw at relegated Watford.
Frank Lampard's side have lost just once in their last six matches to climb out of the relegation zone.
They also have a game in hand on Leeds in the fight for survival.
Jamie Vardy scored twice and James Maddison also netted as Leicester beat relegated Norwich 3-0 at the King Power Stadium to end a run of seven games without a win.
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