Carew struck with a fine header in the 26th minute from a typically brilliant Ashley Young delivery.
And just two minutes later, the big Norwegian caused uncertainty in Albion's defence, allowing Gabby Agbonlahor to strike low past Scott Carson.
The Baggies did get a goal back through James Morrison after a Brad Friedel mistake, but they simply couldn't find a way to restore parity.
Carew again threatened in the second half and hit the post twice in the space of five minutes.
The Villa target man looked refreshed after missing the UEFA Cup clash with Litex in Bulgaria and his rampancy breathed life into the away side.
When Carew doesn't play Villa lack the extra dimension that only he can offer.
The powerful front man is so strong and at times he is unplayable.
West Brom defender Leon Barnett, a last minute replacement for Abdoulaye Meite, had a torrid time against Carew.
Flamboyant
The former Luton man was at fault for both the Villa goals as he lost Carew from a free-kick, which the striker flicked home and then failed to clear properly giving Agbonlahor a run on goal.
Morrison pulled a goal back as Friedel spilt a tame Robert Koren shot from the edge of the area.
And it looked like Friedel's mistake would cost Villa as the home side poured forward, but the American stopper was at his very best moments later.
Do Heon Kim was about to wheel away in celebration but the keeper poked out a giant left hand to deny Albion a goal which would have brought them level.
Villa had further chances to extend their lead in the second half but the first half performance was just enough.
The Claret and Blue now sit fourth in the Premiership and the fans couldn't ask for more after such an impressive derby victory.
John Carew is one man who is feeling the full benefit of Villa's flamboyant football.
And if Villa are to mount a top six challenge, the Hulk will have to stay fit and carry on demolishing opposition defenders in this sort of manner.