The 18-year-old netted twice as the Premier League champions recovered from a goal down to win 2-1 at the Stadium of Light.
Craig Gardner had put the Black Cats ahead after four minutes on Wearside, but United boss David Moyes said that he was happy with how his side reacted following a poor start.
The win ends a run of back-to-back defeats for the Red Devils, although the Scot is not allowing himself to get too carried away.
"I am pleased we have won, I am not going to get too excited," Moyes told Sky Sports News. "I thought we played well with the exception of the opening five or 10 minutes.
"[Januzaj] is a wonderful player, he is someone who we think a lot of. I have tried to get him in the team over the last few weeks but for various reasons it did not happen.
United are ninth in the league.