Not since David Moyes was in charge had the Red Devils achieved that feat, but they made light work of their Turkish opponents thanks largely to two quick-fire first-half penalties after an underwhelming start to the game.
Paul Pogba got the ball rolling for the hosts, coolly tucking away the penalty after a drawn-out run-up, before adding a second later in the half to put his side on their way to a comfortable win which takes them joint-top of Group A.
United, showing seven changes from last time out, actually made a slow start to the contest as they failed to ask any sort of questions of their opponents despite being allowed to dominate possession in the opening quarter of the match.
Pogba had one shot blocked by the head of ex-Liverpool defender Martin Skrtel and Anthony Martial failed to make contact when picked out at the back post, but it was proving to be a frustrating start to the match for the 71,000 spectators inside the Theatre of Dreams - a record attendance for a Europa League group game.
United were soon on their way, though, with Pogba converting the first penalty when Juan Mata was brought down inside the area, before Martial did likewise three minutes later after a push from Sener Ozbayrakli who somehow avoided any further punishment from the referee.
In just his second start of the season, Michael Carrick's pass from midfield proved key in helping to earn the decisive first spot-kick, though his error 38 minutes in nearly gave the visitors a lifeline in the match.
A ponderous piece of play allowed the Yellow Canaries to attack, with Josef de Souza cutting inside and sending a shot towards the bottom corner which David de Gea kept out with his only involvement of the half.
United were able to make sure of the points from the final kick of the opening 45 minutes, as Jesse Lingard teed the ball up for Pogba to curl a screamer into the top corner - his second of the night and third since rejoining the club in a record-breaking move.
If the points were not assured before the interval then they certainly were just moments after the restart - Rooney quickly shifting the ball on for Lingard who in turn picked out the bottom corner for his first European goal.
Much of the pre-match talk had centred around Robin van Persie's return to Old Trafford, where he scored 58 goals in 105 appearances during his days as a United player, yet it took until an hour in for the Dutchman to muster his first shot.
It was a good attempt, though, curling the ball just inches wide of the target with De Gea rooted to his spot, as Fenerbahce continued to struggle to grow into the match.
The Turkish outfit, now managed by former Sunderland boss Dick Advocaat, have made a slow start domestically and were once more below-par tonight, though this thrashing was their first defeat in six outings in all competitions.
The gulf in quality between the two teams was clear to see as the match wore on but the chances dried up after Lingard's fourth, with 77 minutes on the clock before Mata tested Volkan Demirel with the next on-target attempt.
There was still time for the inevitable Van Persie goal late on, thanks to a well-timed run to profit on half-time sub Emmanuel Emenike's pass, leading to ripples of applause from the home fans and from Sir Alex Ferguson - the man who brought him to the club - high up in the stands.