The Hoops took the lead early on and added two more in the second half at Loftus Road to ensure that they kicked off their new Championship season with maximum points.
Onuoha did not know a great deal about it, with the ball simply hitting the defender a yard out and trickling over the line to give the hosts a fourth-minute lead.
Ben Gladwin looked to double his side's advantage when testing Green from a free kick, and the ex-England international was at fault again soon after when fluffing his lines from another wide delivery.
There was almost a moment to forget for Ronaldo Vieira when his clearance cannoned back off Tjaronn Chery and clipped the far post, while Sebastian Polter also cut inside and hit the post in a strong first-half showing for the R's.
Leeds were the side on top for the opening quarter of the second period, without really making their hold on the game count for much in terms of chances.
Chery nearly squeezed the ball past Green as QPR looked to put the game out of reach, while Nasser El Khayat also tried his luck before the second finally arrived 72 minutes in.
After Jordan Cousins was brought down inside the box, Chery stepped up to successfully convert from the spot to put Rangers well on course to an opening-match win.
Marcus Antonsson should have reduced the arrears when bursting through, but he failed to do so and Polter was on hand to add a third goal at the death to round off an afternoon to forget for United.