The Belgian came off the bench to score in what could prove his final appearance for the Toffees at Goodison Park after 115 minutes of an absorbing second-round tie.
Fellaini had received a good reception on his introduction despite continually being linked with a move to Manchester United before next week's transfer deadline.
Team-mate Leighton Baines, who is also interesting United, was an unused substitute but was also applauded as he warmed up.
With the transfer window due to close before Everton's next home game, it remains to be seen whether either play in blue at Goodison again.
Fellaini's close-range strike sent the Merseysiders through to a third-round clash with Fulham.
Yet Stevenage had proved tough opponents and almost snatched victory in the last minute of normal time through boyhood Everton Greg Tansey.
Everton made eight changes and handed out debuts to goalkeeper Joel Robles, defender John Stones and midfielder Deulofeu while Arouna Kone was given his first start.
They proved suprerior to Graham Westley's men in almost all departments - but their finishing let them down.