Tranmere continued their move towards the division two play-off zone with a comfortable victory, although the sending off of QPR striker Paul Furlong in the 36th minute had a major influence on the proceedings.
The visitors had looked the better side before Furlong was red carded for taking a kick at home defender Ian Sharps.
Rovers keeper John Achterberg made important early saves for the Merseysiders, who eventually went ahead after 51 minutes following a quickly taken free kick which resulted in Simon Howarth netting from Alex Hay’s cross.
QPR should have been level two minutes later but the unmarked Danny Shittu headed over from Richard Langley's free-kick.
Stuart Barlow set up Gary Jones for a simple second goal for Tranmere on the hour and Jones struck again with a 71st minute header, with Barlow again the creator.
QPR boss Ian Holloway was left fuming by the performance of referee Mark Cowburn.
"It was one of the worst performances I have seen by an official for a long time," he said.
"He did everything he could to make it comfortable for the home side. I thought we were far and away the better side with eleven men but we lost the plot once their first goal went in from a free kick which should have been our way.
"If my player threw a kick for the sending off he has let us down. The referee changed the whole course of the game. We have lost three nil and it is a very bitter pill to swallow." Home boss Ray Mathias said: "I thought it was an excellent victory. You saw the quality of QPR in the first half and we were not at the races but we performed very well in the second half.
"The sending off was unfortunate and decisions can sometimes change a game."