Having started with a similarly dour 1-0 win over Tottenham at Old Trafford on Saturday, midfielder Januzaj struck in the 29th minute at Villa Park to secure another three points.
Though the performance was far from impressive, United was ultimately rewarded for dominating possession, while the home side was punished for failing to provide any real attacking threat.
“I think we have played better than last week, and it was an away match,” United manager Louis van Gaal said. “I’m very happy… we don’t give many chances away and every game we have more chances than the opponent and that’s the game.”
A 20-year-old squad player who last scored for United in April 2014, Januzaj was the only change to the United side that started against Spurs. Argentina’s Sergio Romero kept his place in goal, with Van Gaal again deciding to rest Real Madrid target David de Gea.
Januzaj, who had struggled to make any impact in the opening stages, broke the deadlock after Mata threaded a clever pass through the left side of the Villa defense.
The United forward showed neat footwork to evade a challenge from Micah Richards before firing a deflected, low shot that glanced in off the base of the far post.
“He scored a wonderful goal, but all the other aspects of football, you have to show it also,” Van Gaal said, highlighting that the Belgium international was also guilty of giving the ball away at times.
United should have made it 2-0 when Mata sent through a long defense-splitting pass in the 73rd, but Memphis Depay’s first-time shot was wide of the target.
Premier League action continues over the weekend, with the highlight being Sunday’s match between the two sides that have won three of the last four titles — Manchester City at home to champion Chelsea.