Having knocked the Hatters out of the Carabao Cup on penalties in midweek, the R's made it two wins in the space of a few days as goals from Nicolas Madsen and Michael Frey turned the contest on its head.
Jimmy Dunne's own goal had given the Hatters an 18th-minute lead but Rob Edwards' side have now taken just one point from four games since being relegated to the Championship.
Edwards took responsibility for his side's poor start to the season.
"It's on me, and it's on us, there's no doubt about it," said Edwards.
"We put ourselves in a great position to win the game, 1-0 up and I thought playing really well in the first half, I thought we were still in really good control until their first goal.
"I thought we should have gone 2-0 up, we had a big, big chance, but that can happen. The goals were really disappointing, I've been saying that for too long and again, it's on me, I'm not blaming anyone.
"People can make mistakes, but then there's got to come a point where we've got to deal with it better.
"It's too easy for them to score the first goal which rocked us for a minute or two, I don't think we should have thrown the ball into Shandon (Baptiste) for the second goal and then we didn't defend the cross."
QPR boss Marti Cifuentes added: "They're a very physical side, they scored, that was the first moment and six or seven minutes of the second half they were very dominant.
"Nardi made a great save to keep us in the game, and after that we made some adjustments, but against a team that pressed so high and being so dynamic, it's about getting the right combination.
"We got to 1-1 and that was the case. We got in behind them, we managed to get the goal which was exceptional and then we were very good.
"We got the second goal, we had good control, the last four or five minutes we came under pressure, but it was a good shift."
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