Sousa was coming up against Rangers for the first time since his contract at Loftus Road was terminated back in April, and it was he who had the last laugh.
After an opening 45 minutes which promised plenty but ultimately delivered just one tame effort on target, the second half provided far more entertainment.
Swans keeper Dorus De Vries was called upon to make two stunning saves before R's captain Martin Rowlands saw red for a second bookable offence. And from then on the game swayed in the home side's favour.
Mark Gower converted Angel Rangel's great cross 16 minutes from time and after QPR midfielder Ben Watson was also shown a second yellow card, Lee Trundle wrapped up all three points with his second goal in three games.
The triumph ended Jim Magilton's six-match unbeaten run in the league and provided Swans with their first league victory over QPR since 1965.
Akos Buzsaky came close to opening the scoring after just three minutes at a sunny but blustery Liberty Stadium, finding the roof of the net with a curling effort from the edge of the penalty area.
A clearly confident R's side, on a high as a result of their impressive form of late, soon settled into their stride and Wayne Routledge was next to go close from 20 yards.
After some patient build-up play, Stephen Dobbie forced Swansea's closest attempt, and arguably the closest of the first half, when his deflected effort at the near post flew narrowly wide.
On-loan Arsenal striker Jay Simpson then fired off target at the other end with QPR enjoying their best chances on the counter, although neither goalkeeper had yet been forced to make a save of any note.
Despite the best efforts of both sides it was becoming evidently clear that a goal for either would really bring the game to life.
Swans midfielder Darren Pratley fired wide while Dobbie drilled straight at Radek Cerny - the first effort of the game on target - as the home side applied pressure in the closing stages of an opening 45 minutes which they had just about shaded.
In stark contrast to the first half, De Vries was called upon to make a superb save just four minutes after the restart.
Watson's corner was flicked on at the near post and the Swans keeper denied Simpson with an instinctive reflex save from close range.
De Vries again had to be at his best just minutes later to produce a superb stop to keep out Routledge in an action-packed start to the second half.
But having twice come close to breaking the deadlock, Rangers were reduced to 10 men in the 53rd minute when skipper Rowlands was shown a deserved second yellow card for a rash challenge on Nathan Dyer.
The dismissal spurred the hosts in action and they immediately put QPR on the back foot, although for all their dominance they were failing to really test Cerny.
Yet that all changed in the 74th minute when the unmarked Gower connected with Rangel's cross to open the scoring from close range.
Watson received a second yellow for handball just minutes later, reducing the visitors to nine men.
And it was left for Trundle to wrap things up when he connected with Dyer's right-wing cross from six yards in the 85th minute.