The 18-year-old Belgian winger, who had earlier been booked for diving, dragged a misfiring United back into the game with a calmly-taken 55th-minute equaliser and then smashed a dipping volley past keeper Keiren Westwood to win the game just six minutes later.
It took the hosts just five minutes to get their noses in front, although the goal arrived courtesy of some calamitous defending which rather set the tone for United's first-half display.
Emanuele Giaccherini tricked his way past Patrice Evra on the Sunderland right all too easily and fired in a cross which Phil Jones thumped straight at team-mate Nemanja Vidic.
David De Gea came to United's rescue 11 minutes before the break when he somehow managed to claw away Giaccherini's goal-bound header with a save of genuine quality.
United's desperation was summed up within three minutes of the restart when Januzaj collapsed in a heap as he went past John O'Shea inside the penalty area and was promptly booked for diving.
But the Belgian was not to be denied and his industry paid off seven minutes later when he played the ball out to Evra on the left and then worked his way into the penalty area to meet the Frenchman's cross with an assured finish.
Then O'Shea got his head to Nani's right-wing cross and the ball dropped nicely for Januzaj, who gleefully dispatched it into the bottom corner with a sweet left-foot volley.