The west Londoners began well, scoring inside 26 seconds when Helguson found the back of the net from about a yard after Schmeichel failed to hold on to Tommy Smith's shot.
Faurlin then tested Kasper Schmeichel with a curling effort from 20 yards that the visiting goalkeeper pushed away to his left.
Leeds were always a threat on the break with Gradel's pace and the Ivory Coast-born player was fractions from scoring when his intended cross from the right had to be pushed over the bar by Cerny.
Their striker Billy Paynter then found himself one-on-one with Matt Connolly before falling over on the edge of the area after the QPR defender stuck out his leg. Referee Mark Clattenburg waved play on, much to the annoyance of the visiting team.
Leeds finally made the breakthrough seven minutes before the break when Richard Naylor's long ball into the area was met first by Gradel, who nudged it past Cerny.
McCormack should have added a second for the visitors after the break but smashed his effort from the edge of the six-yard area high and wide of Cerny's bar.
The Scotland international's persistence paid dividends after the interval when his surge into the area was rounded off with shot that took a deflection off QPR's Kaspars Gorkss.
It temporarily silenced the home crowd inside a packed Loftus Road. Their side did their best to finish the season with at least a point.
Smith forced Schmeichel to tip over his header before the former Watford man brought out another great block from the Leeds stopper. Gorkss then headed a foot wide from the resulting corner.
QPR may have ended the season with a defeat - their sixth in the league - but with smiles on their faces as they look forward to the prospect of playing in the Premier League for the first time since 1996.
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