Swansea moved into the top six of the Barclays Premier League after Ki Sung-yueng finally unlocked QPR's defence to win 2-0 at the Liberty Stadium.
Rangers defended resiliently for 78 minutes before Swansea's top goalscorer Wilfried Bony turned provider and set up the South Korean midfielder for his first Liberty goal, a sweet strike past the previously unbeatable Rob Green.
The goalkeeper had made several excellent stops to keep the scores level but he was beaten again four minutes later when substitute Nathan Dyer set up Rangers old boy Wayne Routledge from just outside the area.
Harry Redknapp showed all his vast experience to set up a Rangers side to frustrate confident Swansea and as the game went into the final quarter it looked as if they might collect the point necessary to escape the bottom three.
But Ki's angled drive off Green's far post and Routledge's third goal of the season added to Rangers' travel sickness which has failed to see them acquire an away point since their promotion.
Rangers had conceded nine goals in their previous two games against Swansea and they might have feared another beating after Niko Krancjar had failed to keep his inviting first-minute free-kick down.
Swansea were slick in possession and determined to stretch the Rangers defence by getting their widemen Wayne Routledge and Jefferson Montero into the game.
Bony's obvious confidence was also reflected in third minute when he slipped Steven Caulker and put Routledge through on goal but Green was quick off his line to smother.
Green made another superb stop when Kyle Bartley was left unmarked from Gylfi Sigurdsson's eighth-minute corner and Bony fired over when a poor Rangers clearance fell at his feet.
Rangers were almost the architects of their own downfall again when Karl Henry lost possession for Montero to cross and Routledge to volley, Yun Suk-young bravely blocking the goalbound effort.
Montero was keen to test his Rangers marker Nedum Onuoha at every opportunity and he started another free-flowing move which ended with Neil Taylor squaring to Sigurdsson and the Icelandic international's shot squirming wide courtesy of a Joey Barton deflection.
Swansea came closest to breaking the deadlock after 37 minutes when Barton was booked for bringing down Routledge and Sigurdsson curled the free-kick around the Rangers wall.
Green dived to his left to keep the shot out with television replays showing how close the ball was to crossing the line, only fractions preventing Swansea from taking the lead.
But having dominated the first half there was almost a nasty sting in the tail for Swansea when Krancjar crossed for Leroy Fer to steal into the box, but his header was sent straight at Lukasz Fabianski on his goal-line.
The first-half pattern of Swansea creating chances but failing to take them continued within three minutes of the restart when Sigurdsson slipped Bony through, but Dunne raced back to block and the ball ended up on the roof of the Rangers' net.
Ashley Williams had to react smartly to stop Eduardo Vargas reaching a loose ball on the edge of the area and Swansea had to stay patient to work their way through a committed Rangers rearguard.
Rangers were relieved when Green flapped at Montero's cross and no Swansea player gambled in the six-yard box, Yun allowed to scramble the ball to safety.
Swansea were really pushing forward now and Bony should have scored when Leon Britton and Routledge combined, but his finish was weak and straight at Green.
Moments later Bony connected far better with Montero's centre but Green made an excellent stop low at his near post.
Rangers got some brief respite when Fer found some space in a crowded penalty area but Bony, of all people, was back in his own six-yard box to deflect the shot over bar.
But their resolute defending was to count for nothing as Swansea finally broke through in the final 12 minutes and Bony was close to adding a third in stoppage time when he struck a post.