The Gunners are now in real danger of seeing FA Cup winners Manchester City 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, who saw referee Michael Oliver turn down a first-half penalty shout and ruled out a close-range header from substitute Marouane Chamakh before Robin van Persie bundled home a consolation, with boos ringing out around the ground at the final whistle.
Villa - who were in need of at least a point to mathematically secure their top-flight status - took the lead after 11 minutes.
A simple high ball from Kyle Walker drifted through 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 the first quarter of an hour.
A slip from Thomas Vermaelen allowed Ashley Young time on the ball and he slipped a pass through to Bent, with full-back Bacary Sagna left appealing for a non-existent offside as the England striker slotted into the bottom corner.
However, Aaron Ramsey felt he should have had a penalty when he was hacked down by Richard Dunne's flying challenge.
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 saw his close-range header ruled out for a push on Walker, with contact looking minimal at best.
Arsenal finally bundled the ball in through Van Persie during the final minute of normal time, but it was too little too late.
Source: PA
Source: PA