Radamel Falcao failed to respond to Louis van Gaal's pre-match challenge to prove himself, but the giant Belgian came off the bench to secure all three points at Loftus Road
United failed to register a shot on target during last weekend's 1-0 defeat at home to Southampton, and Louis van Gaal's team did little to test the league's most porous defense in the opening 45 minutes.
Fellaini was introduced at the interval and, after a remarkable point-blank save from QPR goalkeeper Robert Green denied much-criticized United striker Radamel Falcao, the Belgian netted his third goal of the season with 58 minutes played.
Green's opposite number David de Gea continued his superb individual season by twice thwarting Charlie Austin when the game was goalless and United needed an injury-time strike from another substitute, James Wilson, to make absolutely sure of the points.
Second-bottom QPR is now winless in five outings, while United edges ahead of Southampton into third before the latter takes on Newcastle in Saturday's late kickoff.
QPR boss Harry Redknapp, who dismissed speculation over his future in the build-up, recalled defender Nedum Onuoha and forward Bobby Zamora in place of benched pair Steven Caulker and Adel Taarabt.
There were defensive recalls for United duo Marcos Rojo and Jonny Evans, while Falcao replaced Robin van Persie (ankle).
At his pre-match press conference, Van Gaal urged Falcao to prove his worth to Manchester United and he passed up a glorious opportunity to do just that in the 13th minute.
An arching left-footed pass from Juan Mata unlocked the QPR defense, but Green stood firm to repel Falcao's close-range effort and then diverted the rebound for a corner.
In the 19th minute, Zamora capitalized on sloppy play from Evans to play in Austin, but De Gea denied QPR's top scorer.
The Spain goalkeeper bettered that stop to frustrate Austin again with half an hour played, extending himself to turn a sweetly struck 25-yard effort behind.
There was a change apiece from each side at the break as Caulker and Fellaini replaced Richard Dunne and Mata respectively.
QPR midfielder Leroy Fer should have done better when he towered above the United defense to connect with Joey Barton's 51st-minute free kick, before Green provided a moment to savor.
Angel Di Maria cut back on the right flank to supply a wonderful cross - Falcao seemingly certain to head home, only for Green to push the ball to safety with a razor-sharp reaction.
But there was nothing Green could do when United went ahead.
Wayne Rooney released Antonio Valencia on the right flank and Fellaini took a touch before rifling the wing back's cutback high into the net.
QPR pressed hard for an equalizer - Austin firing wide before Eduardo Vargas woefully wasted an opening on the counterattack having initially pounced on a Rojo error.
There was more misery for Falcao inside the final quarter of an hour as he failed to convert Wilson's low cross with the goal gaping - though Caulker got a crucial touch on the cross. The youngster beat Green at the second attempt to show his illustrious teammate how it was done after De Gea had prevented Vargas from earning a share of the spoils.