Warren Joyce named a strong side for the clash at Old Trafford with Januzaj, Shaw and Anderson all starting and Louis van Gaal watching from the stands.
Januzaj was the star performer, opening the scoring in the 19th minute after playing in Will Keane before sweeping home his return pass with a clinical finish.
Andreas Pereira, an unused substitute against QPR on Sunday, added a second just three minutes later with a half-volley to double the hosts’ lead, from Shaw’s cross.
Januzaj then put the game out of reach just five minutes later, as he skipped past a defender before firing home a composed finish, after good work again from Keane.
Defender Shaw, who did not feature aginst QPR despite being named on the bench, departed at half-time, to be replaced by Ben Pearson, after making his return to action after a hamstring injury.
Januzaj then completed his hat-trick in the 83rd minute, the Belgium international sliding the ball home after a slick exchange in the box, thus rounding off a performance that will surely have impressed the watching Van Gaal ahead of United’s next senior outing against Leicester.