Tottenham made the breakthrough in first-half stoppage time after Kranjcar chased a lost cause.
The ball seemed to be drifting out of play but he managed to get in a cross and Crouch headed home off the underside of the bar.
Blackburn made a bright start to the second half with Benni McCarthy seeing a shot hit the post, before Steven Nzonzi forced a save from Heurelho Gomes.
But Tottenham always looked dangerous on the break and they were unlucky not to go 2-0 when Crouch stooped to head in Aaron Lennon’s cross, only to be flagged offside.
Crouch was not to be denied and got his second goal of the game three minutes later with a cool finish after substitute Jermaine Jenas had created the opening.