Carew and Agbonlahor struck in the space of 90 nightmare first-half seconds for Albion as Villa ground out their third away win in just six days - including a UEFA Cup success against Litex Lovech in Bulgaria on Thursday.
Albion, who have now lost three of their opening five Premier League games, did give themselves hope when James Morrison reduced the arrears in the 34th minute with his second goal in two games.
But the margin of Villa's victory could have been greater as Carew hit the post twice in just two minutes in the second half.
Villa's quick one-two to take command of the game was a personal nightmare for Albion central defender Leon Barnett.
Barnett had been due to start the game on the bench but Abdoulaye Meite was injured in the warm-up and the former Luton Town defender received a late call-up.
He lost track of Carew in the 27th minute when Ashley Young lifted a free-kick into the area and could only stand and stare as the Norway international striker headed home from 12 yards for his fourth goal of the season.
Barnett was still reeling from that setback when he inadvertently set-up Agbonlahor's strike just a minute later.
Under pressure from Carew, Barnett failed to deal with a long ball up field from Ashley Young and his attempted clearance fell invitingly into the path of England Under-21 international marksman Agbonlahor, who surged into the area before beating Scott Carson from an acute angle.
Having taken advantage of two defensive mistakes to take control of the match, it was ironic that Albion were handed a lifeline by an error from Villa goalkeeper Brad Friedel.
There appeared to be little danger when Albion midfielder Robert Koren let fly from 20 yards.
Veteran former America international Friedel got down to save his shot but inexplicably let the ball slip from his grasp and Morrison was on hand to score from six yards.
While Friedel was at fault for Morrison's strike, he went some way to making amends on the stroke of half-time with a stunning one-handed save to retain Villa's advantage.
Paul Robinson whipped in a left-wing cross and Kim headed goalwards only to see Friedel tip the ball to safety with his left hand.
It was a crucial intervention by the former Blackburn Rovers keeper as Albion never seriously tested him again.
It was Villa who continued to look the more potent side as Albion struggled to keep Carew in check.
Carew was picked out by Nigel Reo-Coker in the 50th minute only to see his angled drive hit the post.
Two minutes later, the well-travelled marksman used his height to meet a Luke Young cross only to see his header hit the post.
Carson, who spent last season on loan at Villa, then denied Reo-Coker by tipping his 66th minute drive around the post.