As a result of this belated victory Villa moved back into fifth spot in the Premier League while Hull remain just three points ahead of the drop-zone.
In the circumstances it was hardly a classic and Carew's 34th-minute strike was the one piece of good finishing of the evening and earned Villa automatic entry into Europe next season.
Early in the game Villa, with only four points from their previous six home games, hardly inspired any confidence of an improvement in their form at Villa Park as Hull played with a great deal of urgency to deal with the home team.
Hull, however, suffered an early setback when they lost skipper Ian Ashbee with a leg injury following a challenge for the ball with Gareth Barry.
As usual, Villa played with plenty of flair and imagination but the cutting edge was still missing in another frustrating Villa Park performance.
The nearest to a goal in the early play occurred when Carew's header from a Stiliyan Petrov cross went just wide of the post.
An interested spectator was the England coach, Fabio Capello, who was no doubt running the rule over the Young Player of the Year, Ashley Young.
But the youngster had a quiet time in the first half as the service to the winger was a trifle patchy.
Villa's biggest goal threat up to that point was a James Milner free-kick which was flipped over the bar by former Villa goalkeeper, Boaz Myhill.
But a swiftly executed move originated by Barry ended with an astute cross from Ashley Young which was clinically finished by Carew from close range - his 14th strike of the season.
Hull's defence came under increasing pressure and they were often indebted to the tenacity of Kamil Zayatte in keeping out the likes of Gabby Agbonlahor.
Up front Geovanni was unable to make an impression for the Tigers as he went through an ineffective spell and was substituted at the break following an apparent confrontation with Daniel Cousin as he left the field at half-time.
Myhill, who kept out a good effort from Agbonlahor at the end of the first half, distinguished himself two minutes into the second period with another impressive save from Barry.
The Hull goalkeeper continued in top form as he dived to keep out a Milner blockbuster as the game stagnated when the pace slackened for a spell midway through the half.
His best save came in the 78th minute when he somehow managed to flick Agbonlahor's point-blank header over the bar.