The Black Cats took the lead against the run of play when the visitors launched a scintillating counter-attack and Steven Fletcher beat Rob Green from close range in the 20th minute.
With Reading and Aston Villa facing each other at the Madejski, QPR needed to secure maximum points -and the home side responded through Loic Remy, who netted his third Premier League strike since joining the Hoops.
And QPR secured a vital three points in their bid to beat relegation when Andros Townsend scored his first top-flight goal in the 70th minute, before Jermaine Jenas consolidated the victory just before full-time.
“It was a good day for us,” Redknapp told BBC Sport. “Back-to-back wins for the first time in I don’t know how long. I thought we started well and conceded a goal against the run of play.
“We didn’t feel sorry for ourselves. The crowd were excellent and stayed with us. That was the best I have seen us play. We need to have a run of results like that.”
Meanwhile, QPR owner Tony Fernandes, who provided Redknapp with the funds to sign Jenas, Remy and Townsend in the January transfer window, tweeted his delight at the victory.
Fernandes wrote: “Hehehehehehe. No sleep tonight in Kuala Lumpur. What a win. What a win. What a win.”