They sit three points adrift of safety with three games remaining, but their goal difference is significantly inferior to that of West Ham in 17th and a return to the Championship after two seasons in the Premier League looks increasingly likely.
The Tigers seemed to show a remarkable lack of fight in the closing stages and that was magnified by a hungry and energetic performance from their opponents.
Villa are back to within three points of fourth-placed Tottenham in the race for the final Champions League spot, and on this evidence there is every chance of them winning their final three games to remain in contention.
They have now won each of their last seven league and cup matches against Hull without conceding a goal and their latest victory was richly deserved.
Eyebrows were raised when Hull boss Iain Dowie opted to stick with the 4-5-1 formation deployed in Saturday's goalless draw at Birmingham.
Dowie argued there was no point playing two men up front when his strikers had scored only nine goals between them all season.
But that view looked questionable as Villa dominated possession early on, flooding forward safe in the knowledge that lone-striker Hesselink was the only Hull player in an advanced position.
Stiliyan Petrov, Milner and Ashley Young were all roaming around the midfield with time and space, working the ball to Agbonlahor and John Carew at every opportunity.
It came as no surprise that Villa opened the scoring and the calamitous nature of the goal went some way to explaining why Hull are entrenched in a relegation dogfight for the second successive season.
Petrov clipped a hopeful pass upfield that the hosts had three chances to clear, but Ibrahima Sonko, Steven Mouyokolo and Paul McShane all failed.
The ball ricocheted to Agbonlahor, who McShane had left unattended, and the 23-year-old rifled an unstoppable high finish past Matt Duke.
Dowie's men eventually settled into a tidy rhythm and no sooner had they started to assert themselves on the match, then they should have equalised.
Brad Friedel made a fine double-save to deny Hesselink and Kilbane, who got to the rebound but his poorly-directed shot was deflected over by James Collins with the goal gaping.
It was a chance that Hull could not afford to squander and their evening went from bad to worse after the break when Hesselink was knocked unconscious by a clash of heads with Richard Dunne.
Fortunately, the Dutchman later regained consciousness but with his withdrawal went Hull's threat.
Villa went in search of a second goal and it duly arrived after Carew raced half the length of the pitch before offloading to Milner inside the penalty area.
The England midfielder looked to cut inside but was felled by Boateng's clumsy challenge and picked himself up to send Duke the wrong way from the spot.
Hull must now beat Sunderland at the KC Stadium on Saturday to realistically stand any hope of surviving the drop, while Villa can retain aspirations of top-four finish with victory over local rivals Birmingham at Villa Park on Sunday.
Aston Villa boss Martin O'Neill: "We're in the mix. We're going for everything and guaranteed nothing. We're not even guaranteed to finish eighth in the league at this minute.
"We've gone above Liverpool with three games to go and that's pretty exceptional. But where I've been pleased with the team is they've responded fantastically to the defeat at Stamford Bridge.
"We've come back and taken 10 out of the last 12 points. I think the team has shown a great deal of character all season and I think that was epitomised tonight.
"It was a very professional performance, and I thought we played very well, but at 1-0 the game's still in the balance and it was good to get the second goal, and we saw it through reasonably comfortably."
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