The Belgian latched onto an Ashley Young cross at the back post to nod past Victor Valdes and put Jose Mourinho's side in front at the Riverside Stadium.
Valdes had already made a string of fine saves during the tie before Fellaini opened the scoring on the 30th minute, including a one-on-one from United striker Marcus Rashford.
30 - Marouane Fellaini's strike has ended his run of 30 Premier League appearances without a goal. Opener. pic.twitter.com/aahh1tAHmf— OptaJoe (@OptaJoe) March 19, 2017
20 - Marouane Fellaini's goal versus Middlesbrough means that he's now scored against 20 different teams in the Premier League. Mix.— OptaJoe (@OptaJoe) March 19, 2017
United have not yet lost a Premier League game this season in which they have taken the lead, a run stretches back to an August 2015 fixture away to Swansea.