Mark Gower and Lee Trundle ended Swansea's goal drought as nine-man QPR collapsed in the second half.Dorus De Vries twice saved Swansea at the start of the second half before QPR skipper Martin Rowlands saw red for a lunge at Nathan Dyer, a second booking.
Angel Rangel's ball over the top found Gower, whose half-volley was his first competitive goal for the Swans.
A Ben Watson hand ball saw him off for a second booking in six minutes, then Trundle coolly finished Dyer's cross.
The game was something of a grudge match for Swansea manager Paulo Sousa, who is in a legal dispute with QPR following his departure from the club last April.
Martin Rowlands throws away his skipper's armband after his red cardThe Portuguese boss has seen his Swansea team go four matches unbeaten, but they had failed to score in four of their last five matches.
There was little sign of their woeful scoring record of five goals in 10 games improving in a nevertheless entertaining first half.
Both sides produced some stylish play but rarely threatened to break the deadlock, the best chances falling to Darren Pratley, Stephen Dobbie and Jay Simpson.
The visitors looked like they were beginning to take control after the break, though, Swansea having to rely on Dutch keeper De Vries' fine saves to keep out Simpson and Wayne Routledge.
But then Rowlands - booked for a first-half clash with Dobbie - made his rash challenge on Dyer.
Swansea had not scored in four of their five previous gamesStill the Swans struggled to find a meaningful strike, and few would have looked to Gower, who went the whole of last season without scoring.
Such was the winger's relief at his first Swansea goal that after smashing the ball past Radek Cerny he was churlishly booked for an over-exuberant celebration.
Minutes later Watson saw red for a foolish hand ball, and it was left to fans' favourite Trundle to round off the day.
The on-loan Bristol City striker, a 60th-minute replacement for Thomas Butler, benefited from a pacy breakaway move.
Rangel found Dyer, whose inch-perfect cross was met by Trundle's left-footed strike, his second goal since his return to the Liberty Stadium.
The victory was Swansea's first over QPR in the league since 1965 and ended the visitors' six-game unbeaten run in the Championship.
To complete a perfect day for the home fans, Swansea supporter John Hartson was presented to the Liberty Stadium crowd, the Wales great receiving a fine ovation as he continues his fight against cancer.
Swansea City manager Paulo Sousa:
Sousa hails keeper De Vries
"It was good to get a win against my old club but it was even better to meet up with my old players.
"It is important to beat those teams who are going for promotion as it shows you can win against quality.
"The victory was important with the international break coming up but for 30 minutes it was difficult against them.
"We took full advantage of being against nine players but we are an honest team and never went out looking for yellow cards."
QPR manager Jim Magilton:
"We started really well but should have scored in the first half.
"Swansea came out much better after the interval but their keeper still had to make a couple of great saves to stop us from taking the lead.
"It was two influential players who were dismissed and we carried one or two others but we still tried to play positive football despite the setbacks.
"I felt comfortable for the opening half hour but that lack of a cutting edge has cost us."