Three of manager Redknapp's January acquisitions - French striker Loic Remy, Tottenham Hotspur loan signing Andros Townsend and free transfer Jermaine Jenas - scored for the home side at Loftus Road.
It is the first time since December 1995 that QPR have recorded back-to-back Premier League victories - they also beat Southampton 2-1 last Saturday - and the Londoners are now four points from safety with nine games left in the relegation dogfight.
Relegation rivals Aston Villa also enjoyed a triumphant day, overcoming Reading 2-1 with goals from Christian Benteke and Gabriel Agbonlahor, to move out of the bottom three.
Norwich City's Grant Holt missed an injury-time penalty to allow fifth-from-bottom Southampton to leave Carrow Road with a 0-0 draw while seventh-placed West Bromwich Albion beat League Cup winners Swansea City 2-1 at the Hawthorns.
QPR have 23 points and are now level with second-from-bottom Reading in terms of points and goal difference.
Reading avoided dropping to the foot of the table because they have scored 35 goals this season compared to QPR's 24.
Wigan Athletic, who beat Everton 3-0 in the FA Cup Quarter-Finals on Saturday, slipped into the drop zone as Villa climbed to fourth from bottom on 27 points.
FLETCHER GOAL
Sunderland took the lead at Loftus Road through Scotland striker Steven Fletcher who turned in Adam Johnson's low cross in the 20th minute.
Remy, QPR's eight million pounds signing from Olympique Marseille, equalised on the half-hour by slotting the ball past keeper Simon Mignolet after Townsend's shot had deflected off Sunderland defender John O'Shea.
Townsend gave QPR the lead with a fine half-volley from 20 metres midway through the second half and Jenas, the former Spurs midfielder, grabbed his first Premier League goal since September 2009 when he netted in the last minute.
Redknapp, who took charge at the end of November, said it was the best his team had played.
"It was a good day for us, back-to-back wins for the first time in I don't know how long," he told the BBC. "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."
At the Madejski Stadium, Villa could have been two up on Reading within half an hour but for their profligacy in front of goal.
Benteke hit the crossbar with a header and Andreas Weimann dragged a shot wide with the goal at his mercy.
Villa defender Nathan Baker then showed the forwards how to put the ball in the net after 32 minutes, though unfortunately for manager Paul Lambert, it was his own.
Baker, 21, attempting to clear Jobi McAnuff's cross, managed only to fire the ball past Villa keeper Brad Guzan for one of the more embarrassing own goals of the season.
