Goals by Didier Drogba and Juan Mata either side of half-time 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 strike in the 49th minute proved a major turning point as his shot appeared to have been blocked before the line only for referee Martin Atkinson to award a goal.
In the end the decision did not prove decisive as Chelsea ran riot to give themselves a huge boost before hosting Barcelona in the Champions League semi-finals on Wednesday.
The only negatives were a hamstring injury to central defender David Luiz who went off on a stretcher and disrespectful chanting by some Chelsea fans which forced a pre-match silence to mark the anniversary of the Hillsborough tragedy to be cut short.
"It was a great performance by our team. I think that it's a boost of confidence for us," stand-in manager Roberto Di Matteo told reporters after admitting his side had enjoyed a slice of fortune along the way.
"In this case we were on the lucky side but many times before we have had the game going against us. But we didn't score two we scored five."
UNSTOPPABLE SHOT
Chelsea, bidding to win the FA Cup for a sixth time and the fourth time since 2007, took the lead against the run of play.
Spurs had just began to enjoy some dominance when, in the 43rd minute, Drogba controlled Lampard's lofted forward pass, held off William Gallas and turned to thrash an unstoppable shot past Carlo Cudicini, one of three former Chelsea players wearing Spurs shirts.
It was Drogba's seventh goal in nine appearances at Wembley and knocked the stuffing out of Tottenham who had gone closest to taking the lead.
John Terry, back from a rib injury, blocked Rafael van der Vaart's goalbound header on the line and then Van der Vaart's inswinging pass evaded Spurs striker Emmanuel Adebayor and Chelsea keeper Petr Cech but bounced off the post.
Tottenham began the second half groggily and Mata could have made it 2-0 with a low shot brilliantly saved by Cudicini.
Chelsea did not have to wait long to double their lead.
Cudicini again made a great save to deny Drogba and when the ball broke to Mata he fired goalwards. The ball appeared to be blocked by the keeper and Terry who was prone on the turf.
To the astonishment of Cudicini, the Spurs players and even Terry, the referee Martin Atkinson awarded the goal.
'GREAT PERFORMANCE'
"I thought Mata's strike hit me and didn't go over, but the linesman's seen it and given it," Terry said.
"I honestly don't think it went over the line but the linesman gave it and there's nothing we can do about that.
"Spurs are one of the best sides in the league. It was a great performance and a great result."
