The decision to award a 49th-minute goal to Juan Mata, putting Chelsea 2-0 up, appeared to be wrong after video replays suggested the ball hadn’t crossed the line when it was cleared away by Tottenham defender Benoit Assou-Ekotto.
It added to Didier Drogba’s superb opener just before halftime and although Gareth Bale pulled a goal back in the 56th, Chelsea sealed victory through classy strikes by Ramires, Frank Lampard and Florent Malouda in the final 13 minutes.
Liverpool progressed to the May 5 showpiece, which will also be played at Wembley, by beating Everton 2-1 on Saturday.
The decision to award Mata’s goal, when the game was well-poised and Spurs arguably playing the better football, will be the talking point of a riveting game even though Chelsea ended up winning by a handsome margin.
Referee Martin Atkinson made the decision, not his linesman, even though replays appeared to show the ball hadn’t crossed the line when it was bundled clear by Assou-Ekotto, who was lying on the floor on the goalline along with a mass of other bodies, having been flattened by John Terry as they competed for a high ball.
As Chelsea’s players celebrated in a huddle, Spurs’ players protested vehemently, some heading toward the linesman and others to Atkinson, who could easily have given a foul against Terry before Mata got his shot away.
To their credit, Spurs picked themselves up and reduced the deficit within seven minutes through Bale.
Adebayor sprinted onto a pass from Luka Modric, shrugged off marker David Luiz and rounded Petr Cech before being brought down by the Czech Republic goalkeeper. Atkinson played advantage to allow Bale to sidefoot into the empty net.
Luiz ended up being carried off on a stretcher after pulling up with what appeared a knee injury as Drogba went clear, making the Brazilian a big doubt for the first leg of Chelsea’s Champions League semifinal against Barcelona at Stamford Bridge on Wednesday.
Chelsea defended stoutly thereafter, however, with Gary Cahill - Luiz’s replacement - adapting well to being thrown on.
Ramires grabbed the clinching third goal, running onto Mata’s fine reverse pass and clipping a deft finish over the onrushing Cudicini.
The goal deflated Tottenham, which looked a spent force in the final quarter, and there was still time for Lampard to smash a sensational, dipping 35-yard (meter) free kick past the despairing Cudicini in the 81st.
Malouda, on as a substitute, added a neat fifth after a sublime through-ball by the elusive Mata.
Aside from Luiz’s injury, the other cloud on the day for Chelsea was some chanting by a section of their fans while the rest of the crowd observed a minute’s silence before kickoff for the 96 victims of the Hillsborough Stadium disaster and Livorno midfielder Piermario Morosini, who collapsed and died after suffering a heart attack during a Serie B game in Italy on Saturday.