In the second half, Fellaini's early header made it 3-0, and United were happy to stand off and preserve their energy going into the worldwide break at the very least joint-top of the league.
There are just 10 minutes to go and still time for Fellaini to get that elusive hattrick.
Commenting on compatriot Romelu Lukaku, who netted in the 86th minute for his seventh goal in his first seven Premier League games for the club to equal Andy Cole's record, Fellaini said: "He is a goalscorer, we know that".
This will be United's third win on the trot in the Premier League since their 2-2 draw with Stoke at the beginning of September.
With 10 minutes left to play in the half, Ashley Young fired a ideal cross into the box, and Fellaini doubled his team's advantage.
Roy Hodgson could hardly have been given a more testing start following his appointment as Crystal Palace manager just four games into the new season. United's Romelu Lukaku let the through ball glide through the box. Wilfried Zaha has returned to light training having not played since the opening day defeat to Huddersfield Town, but is not fit enough to feature.
Score predictions ranged from 4-0 all the way to 7-0 and within two minutes and 20 seconds, the hosts had the lead. Mike Dean will be the referee, as it will be his first Manchester United game in the current term.
Crystal Palace: Wayne Hennessey 6, Joel Ward 5, Mamadou Sakho 5, Damien Delaney 5, Patrick van Aanholt 5, Luka Milivojevic 5, Yohan Cabaye 5, Andros Townsend 5, Jason Puncheon 5, Jeffrey Schlupp 5, Bakary Sako 5.