McTominay, captaining United at Old Trafford, headed home Alex Telles' corner in the fifth minute to secure United's 34th victory from their last 36 third-round ties.
It was the Scotland international's fourth goal of the season in all competitions, one short of his best tally in a single campaign (five goals in 37 appearances last term).
"Scott has had a very good season," Solskjaer told BBC Sport. "He is being more and more dangerous, we know he can be a box-to-box midfielder. He should have scored a few more on set-plays before now because he is a monster of a human being. I am very happy he got the goal."