The home side took the lead inside the opening 10 minutes through a moment of brilliance from Chair.
The Moroccan dropped deep to pick up the ball before running at the Leeds defence, cutting in on his right foot and unleashing a powerful drive that deflected off Joe Rodon and past the outstretched arm of Illan Meslier.
Leeds responded well to going behind and almost equalised through Piroe, in for the injured Patrick Bamford, whose left-foot shot forced a fingertip save from Hoops keeper Begovic to turn it behind for a corner.
Chair then blazed over and Dykes headed wide as QPR pressed for a second goal.
The home fans were calling for a penalty as the ball appeared to hit a Leeds hand in the area but it did not matter. Soon after, Andersen darted into the box and whipped a superb left-foot curler past Meslier for his first goal for the club.
Summerville’s crisp right-foot volley was expertly saved by Begovic, with Leeds beginning to play with more purpose in the QPR half after the 30-minute mark.
Georginio Rutter then missed a golden opportunity to halve the deficit at the beginning of the second half as he dragged his shot wide of the near post.
Chair followed up another mazy run with a powerful shot that was headed narrowly wide by Leeds captain Ethan Ampadu, with Jack Colback having his shot from the corner deflected wide of the post as the R's threatened to score a third.
Dykes secured all three points with a glancing header at the near post from Chair’s corner that went through Meslier, before Field was left in too much space to power a header into the top corner via Meslier’s palm to make it 4-0.
Substitute Jaidon Anthony’s speculative shot rolled comfortably into the arms of Begovic in added time to sum up the visitors' night as they were left to contemplate the very real prospect of the Championship play-offs.