The well-built striker created the first two goals for Ashley Young and Gabby Agbonlahor.
Carew then notched the third himself and later won a penalty from which James Milner eventually scored, before the England winger produced the cross from which Carlos Cuellar scored Villa's fifth.
It was a much-needed boost for a Villa side which has often promised much only to disappoint against lower division teams, but they had little trouble chalking up only their second win in seven games.
Bolton, the only team in the Premier League not to keep a clean sheet, were again found wanting in defence and have now conceded 15 goals in their last four matches and they are in obvious trouble.
Villa, meanwhile, were forced to make four changes from the side which played at West Ham in midweek. The most significant was the recall of Nigel Reo-Coker.
It was his first start since the Birmingham City game on September 13 following a training ground confrontation with manager Martin O'Neill.
Reo-Coker was surprisingly made captain when he replaced the suspended Stiliyan Petrov.
Luke Young stepped up for his first game of the season as Wales international James Collins was ruled out with a groin injury.
With only one win from their previous six league games it was imperative for Villa to make as bright start and they responded in fine style with an opening goal from Ashley Young after just five minutes.
Only a minute previously they had threatened danger with Cuellar forcing Jussi Jaaskelainen to make a fine save.
The Trotters keeper was again in action when he pushed out a Carew header from Milner's cross, but Ashley Young was on hand to net his third goal of the season.
This was a bad setback to Bolton's leaky defence. They were subjected to considerable pressure and as a result were unable to advance in any great depth.
Their only serious attack came from a right cross by Matthew Taylor which produced a goalbound header from skipper Kevin Davies but Cuellar was on the line to head clear.
The former Villa central defenders, Gary Cahill and Zat Knight, combined to foil the threat of Agbonlahor and Carew following a somewhat shaky start, but it was only the lull before the storm.
Cahill, however, was at fault in the 42nd minute when he attempted to run the ball out of play.
Carew gained possession and slipped a pass back into the path of Agbonlahor to score with a left-footed shot through the legs of Paul Robinson.
A minute later, Cahill atoned when he went up into the attack and slammed his shot against the post with substitute Johan Elmander hitting home the rebound to put Bolton back into the game.
Any hopes of Bolton springing another surprise was dented in the 53rd minute when Carew's sheer persistence earned the Villa striker his third goal of the season.
Carew collected a Milner pass and then beat both Knight and Cahill to push his shot past Jaaskelainen to notch a goal he richly deserved on his overall play.
In the 71st minute Carew won a penalty when pushed by Davies. Milner took the spot-kick only to see it saved by Jaaskelainen only for Steve Sidwell to hit his shot against the post.
Fortunately for Villa, Milner was on hand to convert the rebound to seal the match and crush Bolton.