The Belgium-born youngster had a hand in both goals as United ended a run of three consecutive defeats to get back on track in the Premier League.
Antonio Valencia opened the scoring just after half-time and Danny Welbeck's sixth goal in as many league games sealed the points to ease the pressure on Moyes.
However, Januzaj was a constant menace with both goals coming following crosses from the 18-year-old, and his contribution impressed his manager.
Moyes told reporters: "Everybody can see what a player we have on our hands. He can play all the positions
"We moved Adnan behind the striker against Sunderland in midweek and he played very well. Adnan can play in all the positions around the front.
"I wanted to see if he'd give us any more creativity, any more chances and help us but at half-time I made my mind up I was going to swap him with Shinji.
"He's been like that since day one. I speak to him a lot and he tells me he can play anywhere. He would have no problem.
"He's not a nervous boy; he needs teaching and understanding because he's still learning the game but his natural talent and ability is up there with the best and I think in time he will prove to be that."
United were not at their best in the first half, but improved after the break and Moyes felt they were worthy winners.
He said: "I thought from the start of the second half we played very well and deservedly scored two goals and maybe could have scored more.
"I'd like to think it's going to improve an awful lot, but you have to start somewhere and I thought today was more like it."