It was a pleasing performance from Carew as he linked up well with Villa's £9million newcomer, Ashley Young.
The little and large show could be the answer to Villa's problems in attack. They appear to have the credentials to hit the high spots for manager Martin O'Neill.
But it was goalkeeper Thomas Sorensen who took the match honours with two breathtaking saves in the last couple of minutes when West Ham also smashed the ball against the bar.
In a hectic do or die finish West Ham suddenly hit Aston Villa with all their artillery after their play dramatically improved when manager Alan Curbishley sent on three substitutes.
Matthew Etherington forced Sorensen to make his first fantastic save and the Dane produced an equally brilliant save to keep out an effort from Calum Davenport.
With Villa reeling on the ropes George McCartney saw his diving header deflected by Wilfred Bouma on to the bar to the huge relief of O'Neill and the Villa fans.
The Villa boss hardly expected to have to endure such frenzied pressure as a desperate West Ham attempted to salvage a draw.
O'Neill had previously only been concerned that Villa have been playing good football, but have struggled to find goalscoring form.
Carew's 36th minute strike raised Villa's hopes of an easy win but it didn't occur in a game which struggled to hit the high notes until the Hammers' sparkling finish.
West Ham's desperation was evident for much of the game and their lack of firepower was even more striking than Villa's until they decided to cut loose.
Adding to their woes was the injury on the half hour to their latest £6million recruit, Matthew Upson, who limped out of the game after 30 minutes with a calf injury.
Villa Park is certainly a jinx ground for the unlucky Upson. On his previous visit last April with Birmingham City he had to be assisted from the pitch before the game started with Achilles tendon trouble which sidelined him for the next eight months.
The latest injury was a twisted ankle which occurred when he was involved in a challenge on Gabby Agbonlahor.
With Villa content to wear down West Ham the only goal of the game came when Young pushed the ball forward to Carew. He controlled the pass before firing home the match winner.
Goalkeeper Roy Carroll was far from happy with his defence. He gave vent to his feelings to such an extent that referee Chris Foy had to tell him to calm down.
Villa, however, failed to capitalise upon their lead. Carew eventually made way for Patrik Berger and this appeared to spark off West Ham's determined late bid.
Villa hit the panic button but managed to hang on to their slender lead and record their second successive home win.