Rovers began well in Monday's Premier League encounter and Christopher Samba headed against the bar before seeing a goal disallowed but it was Stoke who took the lead in the 17th minute through Crouch.
The big striker grabbed his second on the stroke of half-time by finishing off a break and, although substitute David Goodwillie pulled one back with 21 minutes to go, it was not enough to prevent a third successive home defeat for Rovers.
The last time Blackburn played at Ewood Park in a 2-1 defeat by Bolton two weeks ago the abuse aimed at manager Steve Kean reached its peak, but four points from matches against Liverpool and United seem to have earned the Scot some breathing space.
The home fans enthusiastically clapped their team onto the pitch and they almost had a goal to cheer inside five minutes as Stoke goalkeeper Thomas Sorensen missed Morten Gamst Pedersen's corner and Samba headed against the bar.
The ball was cleared for another corner and this time the defender did find the net but referee Lee Mason felt Ayegbeni Yakubu had impeded Sorensen and awarded a free-kick.
Stoke weathered the early storm, though, and in the 17th minute they did what Rovers could not and made it count.
Dean Whitehead clipped a lovely ball into the area and Crouch, who was helped by a slip from Samba, chested it down and planted a volley into the bottom corner for his 100th goal in league football.
Crouch then attempted an ambitious effort from 25 yards that forced Blackburn goalkeeper Mark Bunn into a diving save before Sorensen was also drawn into the action, pushing a shot from dangerman Samba around the post.
Blackburn were having a lot of possession without producing much end product, although David Dunn did test Sorensen with a shot from 20 yards while Yakubu's turn and shot after a free-kick had not been properly cleared flew just wide of the post.
Stoke had been pegged back in their own half for a substantial period of time but they inflicted a potentially killer blow in the 45th minute as Matthew Etherington ran virtually from his own box before crossing for Crouch, who finished the chance in much the same way he had the first.
If Blackburn were to have any chance of taking something from the game they surely had to respond early and Pedersen should have done better than slam a shot well wide when a corner came back to him 10 yards out.
The home fans were beginning to get frustrated at the slow pace of their side's attacks and Crouch would have had a hat-trick had he managed to direct a sharp volley from Jonathan Woodgate's cross on target.
Kean responded by sending on Goodwillie for Radosav Petrovic, and the striker had a chance immediately when a long throw from Pedersen caused trouble but he could not keep his shot down.
Crouch seemed determined to get his third and an ambitious long-ranger was not far away.
An almighty downpour descended on Ewood Park in the 69th minute and suddenly Blackburn were on the scoresheet.
Inevitably, it came from a Pedersen corner, which was headed towards goal by Grant Hanley and Goodwillie eventually turned it in just ahead of Yakubu for his first Premier League goal.
Gael Givet got a warm reception on his return to the side after minor heart surgery when he replaced Adam Henley.
Yakubu has been superb for Rovers this season, netting 13 goals, but only he will know how he failed to equalise in the 79th minute.
A Pedersen long throw fell to the striker virtually on the goal line but Woodgate somehow blocked his shot and the rebound fell into the arms of Sorensen.
Kean's troubles were then summed up as he was felled on the touchline by an accidental tackle from Pedersen and, despite a succession of balls into the box, Rovers could not find a way through.