After a goalless first half, Sebastian Coates and Dirk Kuyt gave the Reds a 2-0 advantage, and what looked like all three points.
However, Mark Hughes’ men fought back admirably, levelling things up through Shaun Derry and Djibril Cisse, before Jamie Mackie grabbed the winner in injury time.
Kenny Dalglish was left shell-shocked by the defeat, but gave QPR credit for their comeback.
“I think for us, we were a little mindful of opinions about how we would play after getting into the semi-finals [of the FA Cup] but I think they started fantastically well,” he told Sky Sports.
“For most of the game they controlled it, they passed it, they moved it. They scored two goals and could have been four or five up by half-time and they weren’t.
“They came out for the second half and started quite brightly again, and they went on and got two goals and out of nowhere they have got three.
“For us, we don’t really have an explanation other than to say they deserve a bit of credit for what they did.
“We should have been out of sight before it even got to that stage. It’s a difficult one to take because there was so much that was very positive about the game,” the Scot concluded.
Liverpool remain in seventh place, whilst QPR move out of the relegation spots and up to 17th position.
By Gareth McKnight