The Scotland international found the net in the fourth minute against Watford at Old Trafford, and despite the occasional scare for the hosts, they managed to keep a clean sheet and secure their passage into the fourth round draw.
McTominay, 24, captained a heavily rotated United side against their opponents from the Championship and he was delighted to win the game.
Asked about captaining the team for the first time, he told the BBC: "When the manager told me it was a surreal moment. I've been here since I had just turned five, so that's 18 or 19 years associated with the club and it is a huge honour."
United manager Ole Gunnar Solskjaer also praised McTominay's performance and his leadership skills.
He said: "Scott has got everything a leader has to have. I wanted to test him by making him captain and see how he would react.
"He delivered and he always does. He was brilliant today. We have always trusted our young men coming through and Scott is one who we believe has the Manchester United DNA in him and knows what it is to be a Manchester United player."
United face Burnley in the Premier League in mid-week, with the Reds looking for a win to go clear at the top of the table.
Solskjaer looks set to make lots of changes to his team once again and could even call on his new signing - 18-year-old winger Amad Diallo, who recently joined the club from Atalanta in Serie A.
Speaking about the new arrival, the United boss said: "As a club, we have followed Amad for a number of years and having watched him myself, I believe he is one of the most exciting young prospects in the game."