Sousa, back at QPR for the first time since being axed as boss, saw his Swansea side take a deserved second-half lead through Nathan Dyer's goal.
A win against his former club would have been sweet for the Portuguese, whose five-month reign was blighted by problems on and off the pitch.
Swansea were the better team for much of the match and twice went close to taking the lead in the opening 20 minutes.
First, Dyer latched onto Shefki Kuqi's ball over the top of the Rangers defence and was unlucky to see his shot bounce back off the inside of the post.
And Rangers had another lucky escape when Dyer again found himself through on goal and Matt Hill almost put the ball into his own net while denying the winger with a last-ditch challenge.
Swansea continued to look dangerous and went close again when Mark Gower's corner was headed over by Ashley Williams, before Guillem Bauza wasted a great chance for the visitors.
QPR's Kaspars Gorkss made a mess of an attempted header clear, allowing Kuqi acres of space on the right wing. Kuqi pulled the ball back for Bauza, who could only fire straight at keeper Carl Ikeme.
Rangers did threaten when the recalled Akos Buzsaky volleyed wide but otherwise Swansea looked more likely to score and continued to dominate after the break.
The home side's luck ran out when Bauza's chip forward struck Hill on the back. The loose ball fell to Dyer, who side-footed home from the edge of the penalty area.
R's boss Neil Warnock responded by sending German on in place of the hapless Tamas Priskin up front and the decision was vindicated when German netted the second league goal of his fledgling career.
Keeper Dorus de Vries flapped at Adel Taarabt's corner and, after Rowan Vine drove the ball back into the six-yard box, German was on hand to score from close range.
Rangers then thought they had gone in front when Taarabt's deflected free-kick was headed into the net by Matt Connolly, but the defender was offside.