Juan Mata, one of Jose Mourinho's five changes from Wednesday's win over CSKA Moscow, struck early on, netting his first Premier League goal since February on his 200th appearance in the competition.
And two close-range finishes from the in-form Fellaini either side of half-time took his season tally to four before Romelu Lukaku sealed a comprehensive victory late on as United continued to impress even without the injured Paul Pogba.
United's win, which saw Marcus Rashford also shine with two assists, moved them top of the Premier League, a position they will keep unless Manchester City can defeat fellow title rivals Chelsea at Stamford Bridge later on Saturday.
Mourinho's side have won seven consecutive matches in all competitions, while Palace are pointless and still without a goal from as many top-flight games as their abysmal start to the campaign goes on.
Palace's confidence was already shot coming into the game and United took advantage to move ahead inside three minutes.
Rashford – another of the stars brought in by Mourinho – was the creator, easily cruising past Joel Ward down the left and cutting back to Mata, who finished simply with his left foot from 12 yards.
A quiet spell followed the early drama, with the next shot on target for either side not coming until after the half-hour mark when David de Gea beat away an effort from Bakary Sako, who was starting in an unfamiliar striking role with Christian Benteke out injured.
United had not tested Wayne Hennessey since their opener, but ruthlessly doubled their lead in the 35th minute. Ashley Young delivered a magnificent in-swinging cross from the left which left Fellaini with an easy task to volley in at the far post.
That buoyed United, with Chris Smalling heading inches wide and Hennessey making a good save from Rashford at his near post as a demoralised Palace side went into the break two behind.
Having struck early in the first half, United repeated the trick within four minutes of the restart. After Young was fouled by Luka Milivojevic, Rashford earned his second assist by whipping in an excellent free-kick from the left and Fellaini made no mistake, heading in from two yards.
Jeffrey Schlupp was angry to have a penalty claim down after a challenge from Smalling at the other end, while Young drew a save from Hennessey as United searched for a fourth.
Lukaku had a quiet outing, but should have scored when he took advantage of an advantage from referee Mike Dean to run into the area and send a left-footed strike inches wide when he appeared destined to find the far corner.
Palace's wait for a goal went on, with Andros Townsend's free-kick flying just wide in their only opportunity in the closing stages, before Anthony Martial was impressively denied by Hennessey after being played in by fellow substitute Ander Herrera.
But United were not to be denied a fourth goal, Lukaku getting his seventh in as many league games by tapping in from six yards after Herrera and Martial had again combined in impressively creating the opportunity.
Key Opta stats:
- Only Halifax Town in 1990-91 (730 minutes) have gone on a longer run from the start of a season in English league history (top four tiers) without a goal than Crystal Palace this season (630 mins). Palace overtook Burnley in 1997-98 (552 mins) in this defeat to United.
- Crystal Palace have lost eight consecutive league games without scoring, the joint-longest run in English league history alongside Hartlepool (two occasions, 1970 and 1993) and Sunderland (1977).
- The Eagles remain the only team in Europe's 'big five' leagues yet to score a goal in league competition this season.
- Manchester United have never lost a Premier League game against Crystal Palace in 17 previous meetings (W14 D3 L0). The Red Devils have set a Premier League record for most games without ever losing to a single opponent.
- Crystal Palace are only the second team to lose their opening seven games in a Premier League season, after Portsmouth in 2009-10.
- No player has scored more goals in their first seven Premier League appearances for Man Utd than Romelu Lukaku (seven - level with Andrew Cole).
- Marouane Fellaini has scored three goals from four shots in the Premier League so far in 2017-18 – more than he netted in the previous two seasons combined, two goals from 46 shots.
- Juan Mata, who made his 200th Premier League appearance (the seventh Spanish player to reach this feat), ended a run of 809 minutes without a PL goal.