The striker levelled to complete his treble with just seven minutes left after QPR looked to have done enough to climb out of the bottom three and leapfrog Villa.
Clint Hill and Charlie Austin had fired Rangers 3-2 ahead after the break following Benteke’s first-half double.
He had cancelled out Matt Phillips’ opener but the draw did little for either side’s survival hopes.
Villa moved three points clear of the Barclays Premier League relegation zone while Rangers climbed to third bottom, still two points from safety.
Jack Grealish made his first league start for Villa as the fit-again Ron Vlaar and Tom Cleverley returned along with Leandro Bacuna and Kieran Richardson.
QPR’s Eduardo Vargas, out for the season with a knee injury, and Yun Suk-young, sidelined with a head injury, were replaced by Niko Kranjcar and Hill.
Villa boss Tim Sherwood had predicted a full-blooded attacking game and Rangers, lifted by their second away win of the season at West Brom on Saturday, fulfilled their part in a breathless first half by opening the scoring after seven minutes.
Austin’s cross was not cleared and Bobby Zamora picked up the pieces to centre for Phillips to nod in unmarked from six yards.
Yet Villa levelled just 151 seconds later when Fabian Delph played in Benteke and the striker was given too much time to cut in from the left and his shot deflected off Steven Caulker and past Rob Green.
The keeper then gathered Grealish’s free-kick as the game reached breakneck speed before the youngster wasted a glorious chance on 16 minutes.
Benteke was set free on the left and when Caulker failed to deal with the cross Green saved at the feet of Grealish.
Villa had recovered from the early setback and were now well on top and Sandro blocked Vlaar’s stinging volley.
But they completed their first-half comeback when Benteke grabbed his second after 33 minutes.
Carlos Sanchez’s tackle on the edge of his own box fell to Gabby Agbonlahor to send Benteke clear.
The striker still had to run the length of the half but he cut inside Hill and sent Green the wrong way with a magnificently composed finish from 16 yards.
Agbonlahor then glanced a header inches wide as Villa looked for a killer third but it never came and they paid the price 10 minutes after the break.
Rangers had offered little threat since going behind but Hill headed in his first Barclays Premier League goal from Phillips’ corner after out-muscling Ciaran Clark.
Deflated, Villa were ragged as they began to give Rangers hope and Brad Guzan saved Austin’s snap-shot on 63 minutes.
The teams looked to be running out of steam before conjuring an epic finale when Austin edged Rangers ahead with 12 minutes left.
Again, Phillips was involved as he wriggled free on the right and found the forward in space to rifle under Guzan from seven yards.
But Benteke clawed Villa back again five minutes later when he curled in a 25-yard free-kick off the post after Charles N’Zogbia had been felled by Hill.