Benteke's free kick with seven minutes to play completed a precious treble and secured a draw that moved hosts Villa up to 16th, three points above the relegation zone while 18th-placed QPR's plight remains perilous.
QPR had taken the lead through Matt Phillips, before Benteke turned the match on its head with his first two goals in the opening 45 minutes.
Veteran Clint Hill levelled shortly after the break with a header and Charlie Austin snatched his 17th goal of the season to restore QPR's lead.
Benteke, however, stepped up to loft his set-piece over the wall and beyond the dive of Rob Green for his seventh goal in his last five league games to round off a pulsating encounter.
“It is always nice to get a hat-trick but it is shame we didn't get the three points. I think we deserved three points, we were better than them,” Benteke told the BBC.
Villa manager Tim Sherwood had described the match as the club's biggest for years and the most crucial of his short managerial career, but his side were hit with an early sucker punch that left them playing catch-up.
Having thumped West Bromwich Albion 4-1 at the weekend QPR were quickly back among the goals as Phillips headed home after seven minutes from Bobby Zamora's clever cross.
The advantage was short-lived as Benteke cut into the area and curled home three minutes later sparking raucous celebrations in the home dugout with Sherwood tearing off his trademark gillet and hurling it to the floor.
The Belgian striker's second arrived 13 minutes before the break with the re-enthused targetman, who had scored only two league goals before February, racing through and finishing confidently.
Villa's home record of three wins all season would have given hope to the visitors as they emerged after the break even with their own record as the league worst travellers.
Hill's leveller arrived 11 minutes after the interval as he powered home a header from a corner, handing momentum back to QPR, who took the lead when Austin's rifled finish found the net from Phillips's cross.
Benteke's leveller however left honours even, with Villa on 29 points with six games remaining, three more than QPR who remain in the drop zone.
Original source: Benteke’s late strike rescues Villa