Eden Hazard came off the bench to send Chelsea into the final of the FA Cup and keep alive Antonio Conte's hopes of winning the double.
The Belgian's low strike from the edge of the area saw the Blues take the lead for the third time in a thrilling game against Tottenham.
Willian struck twice in the first-half with a free-kick and from the penalty spot either side of a superb headed goal from Harry Kane.
Dele Alli scored from close range in the 52nd minute to bring Spurs level for a second time in the game, but they were unable to rouse themselves a third time, with Nemanja Matic applying the finishing touch with a long-range screamer 10 minutes from the end.