Martin Rowlands had received his marching orders eight minutes after half-time and Ben Watson followed him late on to leave the visitors up against it.
For Sousa the victory was particularly sweet after he was sacked by the London club in April.
"It was good to get a win against my old club but it was even better to meet up with my old players," he said.
"It is important to beat those teams who are going for promotion as it shows you can win against quality.
"Today's 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."
Play was evenly matched for an hour, with both sides passing the ball about quickly and to good effect, but the final pass was often poor and few goal chances opened up.
Swansea welcomed back Darren Pratley and Leon Britton to their midfield after spells out injured and it certainly had the desired effect as the home side began to look more like their old selves passing the ball around at pace.
The game changed in the 53rd minute when Rangers skipper Rowlands received a second yellow card after being booked in the first half.
Trundle was sent on after an hour in an attempt to open up the 10 men but worse was to follow for Rangers when Watson was booked twice in five minutes to leave the visitors playing the final 13 minutes with only nine men.
Nathan Dyer, who was prominent down the Swansea right all afternoon, sped down the flank in the 85th minute and crossed low to Trundle, who side-footed home from close range.
Dyer was given plenty of opportunities to show his speed down the wing and, with the defence in fine form, they fully deserved the victory.
Rangers manager Jim Magilton rued his side's failure to take their chances.
"We started really well but should have scored in the first half," he said.
"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 today 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."