The Gunners are now in real danger of seeing FA Cup winners Manchester City, who have a match in hand, overtake them in the race for automatic Champions League qualification after a third defeat in four games.
Bent struck twice inside the opening 15 minutes following more poor defending from Arsene Wenger's men.
1-0: Darren Bent stoops to score the opener
While the Gunners boss will no doubt point to key decisions from referee Michael Oliver to turn down a first-half penalty shout and then rule out a close-range header from substitute Marouane Chamakh before Robin van Persie bundled home a late consolation, the boos which rang out at the final whistle sent a clear message that more of the same next season will not be tolerated.
There were plenty of empty seats at kick-off for the final home match inanother season which promised so much but failed to deliver.
Wenger, though, used his programme notes to urge supporters - some of whom held protests on their way to the ground with thousands then leaving before the players' lap of appreciation - to continue to trust in his young team, and again pledged he would add "what is needed" over the summer.
Flying solo: Bent celebrates his first goal
It was a scrappy start by both sides, with no-one really getting hold of midfield possession.
Villa - who were in need of at least a point to mathematically secure their top-flight status - took the lead on 11 minutes.
A simple high ball from Kyle Walker drifted over Sebastien Squillaci andthrough to an unmarked Bent, who collected it on his chest and turned to volley past Wojciech Szczesny.
Before Arsenal could mount a comeback, they were 2-0 down inside 15 minutes.
2-0: Bent slides the ball under Wojciech Szczesny
A slip from Thomas Vermaelen, on his return from eight months out with an Achilles problem - allowed Ashley Young time on the ball. He slipped apass through to Bent, with full-back Bacary Sagna left appealing for a non-existent offside as the England striker slotted into the bottom corner.
Villa, who had not won for three games, were in complete control as the Gunners - who just two months ago had genuine hopes of success in all competitions - failed to get out of first gear.
However, Aaron Ramsey felt he should have had a penalty when he was hacked down by Richard Dunne's flying challenge after collecting a chip into the Villa box, but despite replays showing no contact with the ball, referee Oliver was unconvinced and waved play on.
All at sea: Szczesny berates Sebastien Squillaci
Van Persie was unfortunate not to be rewarded for his industry when collecting the ball in the left side of the penalty area, and twice turning defenders before a low strike across the face of goal came back off the post.
Arsenal had left the field with boos from disgruntled sections of the Emirates Stadium faithful ringing in their ears - and the substitution of the hapless Squillaci for Morocco striker Chamakh was greeted with sarcastic cheers.
A slip from Alex Song, dropped into the centre-back role, was almost punished as Bent raced clear, but Vermaelen recovered enough ground as the striker's shot-under-pressure was straight at Szczesny.
Down and out: Robin van Persie and Aaron Ramsey look dejected as Bent celebrates his second
Arsenal were camped in Villa's half, yet without finding any creativity in the final third or halted by an offside flag.
When Van Persie did open up the defence after a neat one-two with Kieran Gibbs, Friedel made a smart save at his near post.
The official attendance was given as 60,063 - which those home supporters in the ground could hardly believe given the amount of empty seats, before chants against the 6% ticket price hike rang around the stadium.
Shell-shocked: The Arsenal bench struggle to watch
Szczesny twice denied Villa a third, first from Young's 20-yard effort and then beating away a follow-up from Stewart Downing at the near post.
Chamakh - whose last league goal came against Villa away in November when the Gunners could do no wrong - saw his close-range header ruled out for a push on Walker, with contact looking minimal at best.
Eyes on the ball: Arsenal's Jack Wilshere challenges Stiliyan Petrov
Friedel denied Van Persie after the Dutchman was played in on the right side of the Villa penalty area.
Arsenal finally bundled the ball in through Van Persie during the final minute of normal time, but it was too little too late, as injured captain Cesc Fabregas was left to lead his team around the stadium once more with a sense of what might have been.
Consolation: Robin van Persie pulls one back
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Explore more:People: Robin Van Persie, Darren Bent, Marouane Chamakh, Alex Song, Ashley Young, Cesc Fabregas, Stewart Downing, Bacary Sagna, Thomas Vermaelen, Richard Dunne Places: Morocco, United Kingdom