The Swans had triumphed 5-0 at Loftus Road on the opening day of the season and early strikes from Michu and Rangel set them on their way at the Liberty Stadium.
Substitute Bobby Zamora pulled a goal back for the Rs, only for Pablo Hernandez to restore Swansea's advantage with an excellent finish.
QPR were then denied a clear penalty as referee Neil Swarbrick failed to spot a blatant handball by Ashley Williams, and Michu rubbed salt into the wounds when he added his 18th of the season.
The only downside for the Swans was the loss of Chico Flores to an ankle injury just past the half-hour mark.
The centre-half is set to have a scan to check if he suffered any ligament damage, just two weeks before the Capital One Cup final against Bradford at Wembley.
But QPR, without the injured Loic Remy, have bigger problems as a sluggish start which belied their perilous position at the foot of the table proved very costly.
The visitors had conceded just once in their last five league games, but they were 2-0 down inside 19 minutes after a woeful start.
The opener came in the eighth minute. Nathan Dyer took advantage of the space in front of him to get away a shot, and when Julio Cesar could not hold it Michu was on hand to guide a looping shot in off the outside of his boot and end a run of six games without a goal.
Cesar kept out the forward's low shot from Flores' incisive pass a few minutes later, but it proved a brief respite as Rangel doubled the lead.
Wayne Routledge played the full-back into plenty of space and he slotted his second goal of the season after Cesar could only parry his initial effort.
But Swansea were dealt a blow when they lost Flores in the 33rd minute. The centre-half went in low to make a header and appeared to turn his ankle as he did so and required prolonged treatment before being carried off, with Kyle Bartley his replacement.
The injury did not unsettle Swansea and they continued to have things their own way, with keeper Michel Vorm a spectator throughout the first half.
Clint Hill had a lucky escape when Michu caught him dawdling in possession, as the Swansea man's touch found team-mate Dyer offside.
Adel Taarabt summed up QPR's annoyance when he picked up a needless booking for kicking the ball away when conceding a free-kick, the Moroccan then started a spat with Jonathan de Guzman and Ki Sung-yueng.
Redknapp, deeply unimpressed with the first 45 minutes, sent on Esteban Granero and Zamora for Shaun Derry and Jamie Mackle, and within three minutes his side had a lifeline.
Swansea left-back Ben Davies gifted the ball to Taarabt, and when Vorm could not hold his shot Zamora was on hand to tap in.
But QPR's joy was shortlived as Hernandez struck Swansea's third just two minutes later.
Michu picked out the winger in space on the left, and the former Valencia man did the rest, outfoxing Nedum Onuoha before getting away a shot across Cesar to find the net courtesy of the inside of the far post.
It got worse for QPR when they were denied a clear penalty in the 56th minute.
Swansea skipper Williams clearly handled Andros Townsend's cross, but Swarbrick and his assistants inexplicably missed it, to the fury of the Rangers' bench.
Bartley cleared Stephane Mbia's shot off the line in the confusion, and Swansea piled on the pain when Michu got his second at the end of a sweeping move.
Vorm, Rangel and Kemy Agustien linked to find Hernandez in space, and his slide-rule pass got Michu goal side of Christopher Samba to finish.