A thumping strike from Rafael gave United the lead midway through the first half before Ryan Giggs sealed the win 10 minutes from time against a QPR side who rarely tested opposing goalkeeper David de Gea.
Ashley Young crosses were the chief early threat for United, with Nani failing to connect cleanly from one and Javier Hernandez forcing Julio Cesar to tip over his header from another.
Sloppy play from Cesar almost gifted United a chance on 18 minutes when his roll-out was intercepted by Nani, but the winger’s teasing cross just eluded the stretching Hernandez.
United then took the lead on 23 minutes in spectacular fashion when Rafael arrowed home a brilliant 25-yard volley into the top corner after Cesar had beaten out Robin van Persie’s cross-shot from a narrow angle.
Rafael proved equally adept at the other end as he cleared Chris Samba’s header off the line following a corner after Andros Townsend’s shot had been deflected wide.
The visitors went straight up the pitch, with Rafael again involved as his wonderful cross-field pass was cushioned towards goal by Van Persie, but Cesar produced a superb save down low to his left.
That proved to be Van Persie’s last contribution as he was soon replaced by Danny Welbeck due to injury before the unmarked Nemanja Vidic glanced Giggs’ free-kick wide five minutes before half-time.
QPR’s marking from crosses had been poor in the first half and it continued early in the second when another Young ball in found Nani, whose free header was spilled by Cesar.
Harry Redknapp introduced the returning Loic Remy on the hour mark and within five minutes the January signing was involved as his well-struck shot was pushed away by De Gea.
With 10 minutes to go, United put the game to bed after the QPR defence switched off again and Nani slipped in Giggs to drill his shot beyond the exposed Cesar.
Giggs almost scored his second of the game two minutes later when his impudent looping effort bounced back off the bar and Nani blazed the rebound wildly over, with QPR only offering a late Samba header in response.