Benteke rescued a point for Villa via an 83rd-minute free-kick but Tim Sherwood's men appeared on track for a much-needed victory after leading 2-1 at half-time.
The Belgium international striker's first-half double cancelled out Matt Philipp's seventh-minute opener, only for QPR to hit back with two unanswered goals from Clint Hill and Charlie Austin at Villa Park.
But Villa were not to be denied a priceless point as Benteke stepped up and converted a set-piece seven minutes from time - taking his tally to seven goals in five league matches.
"I wanted more [from the game]. It's always nice to score a hat-trick but it just a shame because we didn't get the three points," he told Sky Sports.
"Today we deserved three points, we were better than them but they were more efficient than us because they got three chances and scored each of them.
"I'm happy [with my second goal], it was success for me. I was good in my game. I wanted to try the free-kick and everything was positive for me tonight."
Villa's draw - their first point following back-to-back defeats to Manchester United and Swansea City - kept the club three points above the drop zone.
QPR occupy the third and final relegation spot with 26 points, the same amount as second-bottom Burnley, while Leicester City are four points adrift.
"The situation is hard, every point is going to be crucial so we need to keep fighting until the end," Benteke added.
"Every game in England is hard, we are going to fight until the end and hopefully we will be safe."
