But, with the North London side chasing the game, Ramires clipped in a third, Frank Lampard buried a super free-kick, and Florent Malouda added a late fifth to send the Blues into the May 5 final against a Liverpool side who have also underachieved in the Premier League this season.
It was not all good news for Roberto Di Matteo though as defender David Luiz was stretchered off after suffering an injury in the move that led to Spurs’ goal, while there could be retrospective action on John Obi Mikel after he kicked out at Scott Parker.
Furthermore, kick-off was preceded by disappointing scenes as a minority of supporters ruined a minute’s silence in tribute to the victims of the Hillsborough stadium disaster and late Livorno midfielder Piermario Morosini, who tragically died during a Serie B match on Saturday.
The match itself started slowly, with the first quarter marked only by Drogba kicking air when put through by a William Gallas slip, and a fine saving tackle from Lampard on Parker.
Then Spurs upped the ante, with greater possession and drive as Salomon Kalou did well to clear from Ledley King; Chelsea were lively on the break though, Mata’s poor touch letting him down when played in by Kalou - a rare error for the man-of-the-match Spaniard - and a Drogba header well blocked by King.
Things started to get really interesting just after the half-hour mark, as Aaron Lennon elected to stay on his feet after a clumsy challenge from Luiz, the England winger’s honesty not matched by his final ball, which was poor.
Then John Terry cleared off the line after Rafael van der Vaart beat Cech with a header from Lennon’s cross, with the Dutchman also hitting the post as his long ball evaded both Adebayor and a stranded Cech.
Terry put in another brave block to keep a Modric shot away from goal, and within a minute Chelsea were ahead.
It was some goal too, but perhaps predictable: Drogba likes to score at Wembley, in Cup semi-finals and against Spurs, his thunderbolt left-footer after chesting a long ball and turning past Gallas a delight just before half-time.
The second half picked up where the first left off, played at breakneck speed with former Chelsea keeper Carlo Cudicini pulling out a fine stop to deny Mata.
From the resultant corner Chelsea went two up with a goal that never should have been awarded. Cudicini had done well to keep out a Luiz header and, in the scramble that followed, Mata drilled a low shot towards goal.
Cudicini was stranded with both Terry and Assou-Ekotto on the line: the latter’s body was in the goal, but his feet and lower legs were clearly outside as he knocked it clear. Atkinson somehow decided the ball had crossed the line and awarded the goal, his assistant unable to help with his vision obscured by the sea of bodies.
The exact nature of the Spurs defender’s intervention was only made fully clear on video replays, but it is unclear just what Atkinson saw to award the goal, yet another goal0
Spurs responded well and they pulled one back six minutes after that blow: Luka Modric sent Adebayor through, the Togolese rounding Cech, who brought him down but escaped a red card because Bale was on hand to finish anyway.
It was game on again and King almost diverted a header past Cech from a corner: but, as Spurs left gaps at the back, Ramires extended Chelsea’s lead with a clever run and touch to meet Mata’s lovely pass, clipping the ball over Cudicini to restore the two-goal lead.
The scoreline got harsher for Spurs as Lampard curled in a fantastic long-range free-kick with eight minutes left, although Cudicini was a shade out of position, and the rout was completed deep into injury time when Malouda slid the ball home from another fine Mata pass.
That came just after Parker and Mikel tangled, the former incensed after the latter reacted to a tackle with a clear kick that Atkinson appeared to miss.
There may be some fall-out from that but, for now, Chelsea celebrate a place in the final.