Early strikes from Michu and Angel Rangel set the hosts on their way. Substitute Bobby Zamora pulled a goal back for the R's, only for Pablo Hernandez to restore Swansea's advantage with an excellent finish before Michu added his 18th of the season.
Defeat means QPR, who were again without Loic Remy, remain rooted firmly to the foot of the Premier League table, still six points adrift of safety with 12 games remaining.
Remy was not risked due to a groin injury but Cesar had played with a similar injury.
It was a gamble which did not pay off as Cesar looked ill at ease dealing with any passes back to him and his failure to hold shots from Nathan Dyer and Rangel led to Swansea's first two goals. The Brazilian should also not have been beaten by Hernandez from a very tight angle.
Redknapp said: "We gave some bad goals away, I can't look at them and say they were particularly good, there were some bad errors.
"Our keeper has been fantastic, probably as good as any goalie in the league, but he played with a groin strain because he felt he was okay but obviously he wasn't at his best.
"He felt he was fine and I can only go by what he tells me, I was told he was okay. He had a problem kicking and obviously when we passed the ball back he got himself under pressure. But in the previous five games when we have done well he has played well but he had a bad day, that's how it goes."
But Redknapp remains confident the R's can avoid the drop.
He added: "We have 12 games left and we have to win as many as we can, I would say we have to win six at least. We have got to keep believing, if you give up what chance have you got?"
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- Angel Rangel