Crouch gave Spurs the perfect start when he headed home Gareth Bale's cross with just five minutes on the clock to level on aggregate.
And it got even better for Harry Redknapp's men just after the half-hour mark when Jermain Defoe latched on to Bale's cross and superbly fired in off the post to put Spurs ahead for the first time in the tie.
Defoe should have stretched the lead further when Aaron Lennon slipped him through, but he put his shot wide, while Crouch was denied from close range after the break.
Crouch did not have to wait much longer for his second, though, when he powered home a header from a corner just after the hour mark.
And after Senad Lulic saw red for a foul on the impressive Bale, Crouch completed his treble from the spot and sealed a 6-3 aggregate win.
Source: PA