Queens Park Rangers have been ridiculed as reckless spenders but a couple of bargains hunted from Harry Redknapp's former employers helped boost the club's prospects of saving their season. Andros Townsend and Jermaine Jenas, the former a January loanee from Tottenham Hotspur and the latter a free signing, scored second-half goals as QPR recorded back-to-back victories in the Premier League for the first time since their promotion two years ago. They remain bottom but only on goal difference and are four points from 17th-placed Aston Villa, whom they face next Saturday. Redknapp's mission improbable looks eminently manageable.

"It's on now, we've given ourselves a chance," said Redknapp, who warned that his side's revival means teams who thought they had little to fear may yet find themselves dragged back into danger. "Even teams on 30 points could get sucked in. You can easily go nine or 10 games without a win so anyone can go on a bad run." Sunderland, who were mainly woeful and have now failed to win in six league games, know that is true.

While others worry about downward spirals, Redknapp came into this game hoping to harness the power of momentum. His claims that QPR could survive were looking like the cant of a crank until last Saturday's win at Southampton. Their bid to build on that was boosted by Bobby Zamora declaring himself fit despite ongoing hip and ankle trouble and could therefore partner the club's most expensive January recruit, Loïc Rémy, for the first time. Redknapp has described that as his "dream" striking duo and with QPR having fired blanks in their last five home matches, he needed that fantasy to come true.

Zamora's inclusion was one of four changes to the line-up that started at St Mary's – and there was no place even on the bench for Adel Taarabt, whose inability to overcome an injury sustained in training in midweek was pointedly mentioned by Redknapp alongside tributes to Zamora's determination to play.

Rangers began like a team who believed survival was within their grasp. Sunderland began like a team who were not sure of anything. There was an ominous servility about the visitors, who lapsed too readily into the role of subordinates. These Black Cats have no lionhearts.

With Junior Hoillet and Townsend deployed as wingers either side of Zamora and Rémy, QPR streamed forward from the outset, eager to get to work on the visitors' makeshift full-backs, Craig Gardner and Jack Colback. Hoillet nearly scored in the third minute thanks to encouragingly intuitive interplay between Zamora and Rémy, the Frenchman reading his partner's clever dummy to collect the ball and feed Hoillet, who fired fractionally wide from 15 yards.

QPR continued to threaten but then, after 20 minutes, Sunderland hit back with a sucker punch. Simon Mignolet bundled away a QPR free-kick and the visitors launched a counterattack. Stéphane Sessègnon dribbled delightfully down the right before crossing to Adam Johnson on the far side of the box. With the defence still lumbering back from the other end, Johnson's cross-cum-shot was turned into the net by the unmarked Fletcher.

QPR had not won any of the matches in which they have fallen behind this season and the Loftus Road faithful would have been forgiven for fearing a collapse. Instead Rangers rallied and they were level within 10 minutes. It took a dollop of luck to help them, as Townsend's 25-yard shot deflected off John O'Shea into the path of Rémy, who slotted calmly into the net. It was his third goal in four starts since his arrival in January and QPR's first home goal since Boxing Day.

They immediately went in search of another, Rémy volleying over from eight yards after a smart nod-down from Zamora. Stéphane Mbia then rasped Mignolet's hands with a 25-yard drive.

Martin O'Neill adjusted his formation to give his side more solidity in midfield and they stemmed the flow towards their goals. The game became stodgy.

The impressive Townsend provided the first threat of the second half, racing in-field off the right flank to smash another left-foot shot at goal – again it was blocked by a defender but this time did not bounce obligingly to Rémy. Four minutes later Townsend ensured victory by unleashing a shot that no one could block. After a cross from the right was headed out of the box, the 21-year-old controlled the ball with his chest and sent a dipping, swirling volley into the net from 25 yards. Sunderland showed no signs of mounting a comeback and QPR helped themselves to a third goal when Jenas, on as an 80th-minute substitute, blaze the ball into the bottom corner from 20 yards.

"That's the best I've seen us playing going forward," said Redknapp. "We played 4-2-4 and went for it and I knew we would either win or get turned over because we were so open. We just have to keep being positive."

O'Neill knows his side are in trouble if they do not get into a similar groove soon. "It's been tough going," he admitted. "But it's up to us to change it around quick."