The hosts lacked ideas and barely created a chance of note as their disastrous season took another turn for the worst, with the club having now taken just seven points from the last 33 available.
Scunthorpe, by contrast, are in fine shape and claimed their third win in four Championship games to give themselves a wonderful chance of beating the drop.
And they deserved victory because they had the best player on the pitch in striker Gary Hooper, who terrorised QPR defenders Kaspars Gorkss and Matthew Hill.
Unsurprisingly, it was Hooper who provided the decisive moment after tying Hill up in knots before laying the ball in to Thompson and giving the winger all the time in the world to pick his spot pas the over-exposed Carl Ikeme with 17 minutes left.
It was only Ikeme's fine reactions that had prevented Hooper from opening the scoring ten minutes earlier after referee Grant Hegley had accidentally blocked Matthew Connolly's attempted clearance.
The ball fell to the in-form hitman only for the goalkeeper to bravely block.
It was only in the final 20 minutes that this game started to catch light, with the first-half being 45 minutes no-one will remember.
Jay Simpson put the ball in the net for the hosts but his celebrations were cut short by an offside flag, while Sam Togwell shot widely over for Scunthorpe from just eight yards.
QPR, with caretaker boss Mick Harford in charge of his first home game, brightened up slightly at the beginning of the second period with Gorkss heading narrowly over and Simpson testing visiting goalkeeper Joe Murphy, but the home' defence was shaky with Wednesday's 5-0 defeat at Nottingham Forest clearly still on their minds.
And that was demonstrated when Hooper left Hill with twisted blood before playing in Thompson to score.
A number of the home fans decided to leave then and they certainly didn't miss much as QPR never looked like getting back on level terms.
As their season reached a new low the home players were booed off, leaving Harford with a salvage job on his hands for the remainder of the season.