Goals by Didier Drogba and Juan Mata either side of halftime put Chelsea in command before Gareth Bale replied for Spurs but Ramires, Frank Lampard and Florent Malouda struck again for the Blues, who will meet Liverpool in the final next month.
Mata's goal in the 49th minute proved the major talking point as his shot appeared to have been blocked before crossing the line only for referee Martin Atkinson to award the goal.
In the end the decision did not prove decisive as Chelsea ran out easy winners to give themselves a boost before hosting Barcelona in the Champions League semi-finals on Wednesday.
Drogba had given Chelsea the lead just before halftime with a thunderbolt shot and Mata's contentious effort put Chelsea in charge.
Bale scored into an empty goal after Petr Cech had sent Emmanuel Adebayor tumbling after 56 minutes to give Spurs hope.
However, Ramires dinked home a third for Chelsea after 77 minutes and Lampard's superb free kick had the Spurs fans heading for the exits long before the end.
Malouda completed the rout in stoppage time.
