Leicester's former Rangers manager Ian Holloway endured a miserable return to Loftus Road and Hayles - recently signed from Plymouth - barely troubled the home defence.
Goals from Damion Stewart, Adam Bolder and Dexter Blackstock put QPR in command, before Iain Hume pulled one back for the Foxes.
Howard, signed from Derby initially on loan so that he could play on the eve of the transfer window opening, came on as a 32nd-minute substitute with Leicester already 2-0 down.
Stewart's header from Akos Buzsaky's corner - the Jamaican defender's fourth goal in seven matches - gave Rangers the lead after a quarter of an hour.
The London side went further ahead when Blackstock headed Rowan Vine's left-wing cross into the path of skipper Bolder, who nodded in from close range.
Howard tried to galvanise his new team and very nearly scored a spectacular goal four minutes into the second half, when his searing 35-yard drive smashed against the post with keeper Lee Camp beaten.
Rangers' let-off proved to be crucial because eight minutes later, they went 3-0 up.
Again a left-wing cross from Vine did the damage, this time enabling Blackstock to head home his first goal since the opening day of the season.
Hume's sweetly-struck free-kick from 30 yards out gave Leicester hope, but they never looked like coming back and Howard missed a great chance when he headed wide late on.
Matt Fryatt was guilty of an even worse miss. The striker headed straight at Camp from inside the six-yard box when it looked easier to score.