Victor Lindelof’s pinpoint pass from defence caught the Granada defence off-guard half an hour into the contest, with Rashford breaking the offside trap, taking a brilliant first touch and calmly slotting home.
The goal could be said to have been against the run of play, but only because there was not much play to speak of.
Granada offered a spirited battle but were short of quality to test David de Gea – in goal for Dean Henderson – and that one moment of quality between Lindelof and Rashford deserved to win the contest alone.
United added to their advantage as Fernandes won and scored a late penalty, though Granada goalkeeper Rui Silva will feel he should have kept out the tame spot-kick.
The Red Devils now take two valuable away goals back to Old Trafford for the second leg, but Solskjaer will be without captain Harry Maguire, Luke Shaw and Scott McTominay, who are all suspended after picking up bookings in Spain.