The Belgian midfielder returned to the Toffees line-up following suspension and produced the leveling goal in the 28th minute after Theo Walcott gave the Gunners a rapid-fire start.
Fellaini pounced on an Arsenal defensive error before unleashing a low, curling left-footed effort past Wojciech Szczesny and into the back of the net for his seventh Premier League goal of the campaign and his efforts did not go unnoticed by Moyes.
"I thought he was fabulous tonight," he told Sky Sports. "But our whole team played well, as we had to do against Arsenal.
"Overall I was really pleased with how the players played.
"Arsenal played well, they had some moments but great credit to our lads after going a goal down after 50 seconds to get right back in it.
"I thought we deserved it when we scored, we were playing well, and it was a really good goal by Marouane."