After dominating the opening stages, Michu gave the Swans the lead when his miss-hit rebound looped in.
The second was far too easy for the home side, as Angel Rangel ran in behind the visiting defence, and had time for two bites at the cherry to put his side 2-0 up.
Substitute Bobby Zamora had given QPR hope early in the second half, but Pablo Hernandez's sneaky third and a wonderful team goal sealed victory at a canter for Michael Laudrup's side, who are up to seventh with this result, and piled more misery on the hapless Rs.
With their Capital One Cup final on the horizon, you could have forgiven the Swansea players if they weren't completely focused on the task at hand, but right from the word go, they controlled the match.
After having the large majority of possession early on, the Swans went ahead thanks to their prolific Spaniard. Nathan Dyer made room for a shot, which could only be pushed out to Michu by Julio Cesar, whose sliced effort from close in only just crept under the bar.
However, the second 10 minutes later had no fortune about it. Rangel got in behind the defence, strolled into the box unchallenged and reacted quickest after Cesar had blocked his first attempt to tap in.
The rest of the first half was a procession for the Welshmen, who passed it around with ease, and were never really threatened by the Rs.
However, a double substitution reaped immediate rewards for Redknapp after the break, as Zamora announced himself by side-footing in yet another rebound after Michel Vorm had palmed Adel Taarabt's shot into his path.
But almost straight away, Hernandez waltzed his way into the QPR box and managed to find the net from an acute angle to restore the Swans' two-goal advantage.
QPR were denied a clear penalty when Ashley Williams seemed to handle Andros Townsend's cross, and the Swans rubbed salt in the wounds with a flowing team goal to seal the win.
After a great link-up between Rangel and Kemy Agustien, Hernandez slid a delightful through-ball into the irrepressible Michu's path, who flicked the ball past the onrushing Cesar.
Substitute Shaun Wright-Phillips saw his stunning volley come back off the crossbar and it just wasn't to be QPR's day.