The Belgian midfielder scored the opener with a header from inside the box in the 34th minute and Jesse Lingard added a second in the 62nd minute. Rudy Gestede netted for Boro in the 72nd minute, before Antonio Valencia added a third for United late on.
And former England star Lineker was clearly impressed with Fellaini’s finish as he compared the midfielder to the suspended Zlatan Ibrahimovic.
Lineker tweeted: “Is that Zlatan with a Fellaini wig?”
And he added after Lingard’s strike: “Superb strike from Lingard as Boro drop their guard.”
Meanwhile, Team GB star Dai Greene was delighted to see Fellaini net the opener, as he tweeted: “So nice seeing a midfielder getting in the box for Man Utd. Great cross and great goal.”
Manchester United headed into the game on the back of their 1-0 win over Rostov in the Europa League last week as they secured their place in the quarter-finals, where they will face Anderlecht.
Next up for Manchester United in the Premier League is a home clash against West Brom on 1 April after the forthcoming international break.
The Red Devils finished fifth and won the FA Cup last season before Jose Mourinho’s appointment at Old Trafford.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news