The midfielder netted for the first time since April 2014 to settle an uneventful game which the visitors comfortably controlled.
United have now not lost at Villa Park in the Barclays Premier League since a 3-1 defeat in August 1995.
Villa rarely looked like hitting back, Jordan Ayew shooting over from distance, as their wait for a home win over United continued.
The result sealed back-to-back victories for United this season and consecutive clean sheets for Sergio Romero who kept his place ahead of David de Gea with the Spain keeper’s future in doubt.
Januzaj made his first start for United since February in their only change from the 1-0 win over Tottenham and justified his recall after 29 minutes of a slow-burning game.
United had already begun to take control but the 20-year-old ensured their patience paid off with a cool winner.
Juan Mata’s defence-splitting pass was perfect for the run of the Belgian who outfoxed the sliding Micah Richards with a smart turn.
He still had plenty to do from the corner of the six-yard box but his shot took a slight touch off Ciaran Clark before going in off the far post.
There had been little previous action with Brad Guzan mopping up from Memphis Depay while Morgan Schneiderlin was caught sleeping while unmarked at the far post.
The goal did, though, rock Villa’s momentum and, aside from a bright opening five minutes, they failed to recover from the blow.
United were prepared to maintain their patient build-up with Villa limited to sporadic breaks which routinely came to nothing.
Ayew, one of Villa’s 10 summer buys, shot over two minutes after the break when the sloppy Mata gifted him possession but Romero remained untroubled.
The hosts had upped their pedestrian tempo after the re-start with Romero gathering Gabriel Agbonlahor’s header, and United reacted by replacing Michael Carrick with Bastian Schweinsteiger while for Villa Rudy Gestede made his home debut for Scott Sinclair.
United had lost their first-half fluency, a testament to Villa’s increased efforts in midfield, although hardly looked in danger of losing their lead.
And they should have doubled it - finishing the game off - with 18 minutes left when Memphis missed a golden chance.
Again it was Mata with the exquisite pass to send the Holland international clear but his first-time curling effort from the edge of the box bounced just wide of the post.
It was a huge let off for limp Villa but one they failed cash in on as United, marshalled by the excellent Chris Smalling, cruised to the final whistle with minimum fuss.