But Bent was starved of service as the visitors, for all their neat and tidy build-up play, lacked penetration in the final third.
Steve BowerBBC Match of the Day commentator
"Fulham were not at their fluent best, but they did enough and it was the unlikely source of Chris Baird who won it for the home team in the end. Although they clinched their fourth win of the season, it could have only been a point had Christian Benteke not missed the chance to equalise. But Villa have now lost five times under Paul Lambert."
And they were made to pay the price as their resistance was finally ended six minutes from time by a rare goal from Baird.
In contrast to Villa's lack of goalscoring threat Fulham looked dangerous from the off, with Dimitar Berbatov again inspiring the Cottagers following his summer move from Manchester United.
The hosts were quickly into their stride in a high-tempo start and it was Berbatov pulling all the strings.
Aston Villa didn't deserve loss says manager Paul Lambert
Villa goalkeeper Brad Guzan had to be alert in the opening stages to parry the Bulgarian's fierce shot from a tight angle, before denying Kieran Richardson from close range with his legs after intricate build-up play involving Berbatov and Sascha Riether.
Guzan continued to be the busiest of the two goalkeepers as Villa failed to stretch Fulham stopper Mark Schwarzer.
But Fulham began to lose their fluency after the half-time break, allowing the visitors to grow in confidence as they gained a foothold in the match.
Agbonlahor could not flick Stephen Ireland's cross goalwards before heading over another right-wing centre from Bent at the far post.
Lambert would have been happier with a point than Fulham counterpart Martin Jol, but the visiting boss was left ruing his luck after Baird scored only the third goal of his Cottagers career.
Fulham's home sweet home
Martin Jol's men have won 10 and drawn two of their 14 matches at Craven Cottage in 2012.
Arsenal (W 2-1)
Blackburn (W 5-2)
West Brom (D 1-1)
Stoke (W 2-1)
Wolves (W 5-0)
Swansea (L 0-3)
Norwich (W 2-1)
Chelsea (D 1-1)
Wigan (W 2-1)
Sunderland (W 2-1)
Norwich (W 5-0)
West Brom (W 3-0)
Man City (L 1-2)
Aston Villa (W 1-0)
And it means Villa are now winless in their last 12 Premier League away matches, spanning nine months, since beating Black Country rivals Wolves in January.
Fulham boss Martin Jol:
"It was a bit of a relief. At the end to score from a corner kick sums it up - scrappy. But we grinded out a result, which is good for us.
"At home I would like to see us dominate and get the goal - that's not what we did today. But I'm happy to get the three points.
"Chris Baird is very good at attacking the near post, he is always close but he hasn't scored for as long as I have known him.
"I was happy to see him score - especially because the corner kick probably was not the best."
Aston Villa manager Paul Lambert:
"I thought some of the football we played was great. I thought we gave as good as we got.
"We came here, where their form has been really good, and gave a good account of ourselves.
"There are a lot of good things. We have to turn the good things into wins. But to concede from a set-piece was disappointing."
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