Fellaini was a menace to the United defence all night and capped an impressive all-round performance with the winner, an unstoppable bullet header from Darron Gibson's corner.
The Belgian, however, was quick to pay tribute to the team effort this evening as they won their opening fixture for the first time in five seasons.
"It was a good goal, it was a good cross, a good corner. It was good for me and for Everton," Fellaini told Sky Sports 1.
"Everton had a lot of chances in the first half and we had to keep going and hoped the team scored.
"I think everybody was motivated. Manchester United is a great club. Everybody is motivated, and I think today everybody played well."
Phil Jagielka was also quick to salute the team effort tonight and urged Everton to carry their momentum into Saturday's clash at Aston Villa.
"We knew it was a great team like Man United but fortunately the big man (Fellaini) put his head where it hurts and we had something to hang on to," said Jagielka.
"I think the whole team was a bit tired towards the end but the effort that we all put in towards the end was fantastic and it's nice to send the Everton fans on the first day of our season home with a win and not the doom and gloom we normally start with.
"It's a fantastic start for us, three points. We'll build on it for the next game, we've got a big game coming up over the weekend so if we can get another point away at Villa, or three, it's going to be fantastic start and hopefully instead of chasing the teams, we can maybe chased for once."
