Ole Gunnar Solskjaer's men were woefully inept in the 3-1 Carabao Cup semi-final first-leg loss at Etihad Stadium, but on Sunday (AEDT) they found their groove, playing some eye-catching football en route to a straightforward win.
Norwich, which was without injured talismanic forward Teemu Pukki, rarely troubled United in a first half dominated by the home side, which went into the interval 1-0 up after Mata teed up Rashford.
Rashford got his second from the penalty spot early in the second period, before Mata, starting only a third Premier League game since the start of October, set up Anthony Martial to extend the lead and Mason Greenwood finished Norwich off, as United held on to fifth place to stay five points adrift of Chelsea.
Despite establishing control almost immediately, United struggled to create clear chances during the early exchanges.
But Juan Mata carved the Canaries open in the 27th minute, cutting in off the right flank and playing a lofted pass towards the back post for Rashford to turn in.
Norwich highlighted the precariousness off United's slender lead just before the break, when David de Gea just about reached Todd Cantwell's curling effort.
Tim Krul was less impressive at the other end just after the break, however, rushing out and sending Brandon Williams tumbling in the box, allowing Rashford to sweep home the resulting penalty.
Martial got in on the act two minutes later, heading in Mata's right-wing cross after Norwich switched off at a corner.
Williams should have increased the lead when he blazed over from a couple of yards out, but there was to be another moment for United to savour, as Greenwood, Rashford's replacement, drilled into the bottom-right corner from 20 yards to wrap up the win in 76th minute.