The 24-year old German-born American midfielder opened the scoring for the Royals in the 10th minute at Loftus Road when he played the ball to Adam Le Fondre before getting on the end of his cross to head home unmarked past Robert Green.
Alex Pearce put the Royals ahead when he nodded home Jobi McAnuff's corner, two minutes before Garath McCleary then produced a stunning 25-yard effort in the 58th minute to all but wrap up proceedings.
A red card to Royals defender Kaspars Gorkss 20 minutes from time gave QPR some hope but the damage had been done as Nigel Adkins' side remained sixth, four points clear in the playoff positions, while Harry Redknapp's charges fell four behind second-placed Burnley.
The goal for USA international Williams was his second this season with his first in the Championship coming in the 3-0 victory at Millwall at the beginning of the month.
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