United only needed a point to progress but Henrikh Mkhitaryan's first goal for the club set them on the way to a comfortable win, which was sealed later Zlatan Ibrahimovic's well taken finish here on Thursday.
Elsewhere in Group A, Fenerbahce triumphed 1-0 at Feyenoord, meaning United will go into Monday's draw as group runners-up.
United coach Mourinho made six changes to the team. Sergio Romero replaced David De Gea in goal, while Eric Bailly made his first appearance in the defence since October following a knee injury. Ashley Young, Daley Blind, Juan Mata and Wayne Rooney also came into the side, according to Manchester United's website.
United's best chances of the half came as the interval neared.
The second half began with United continuing to dominate and a reward duly arrived in the 48th minute when Mkhitaryan opened his United account with a fine goal.
After United won possession in midfield, the Armenian captain headed forward and waltzed through the Zorya defence, shimmying past a couple of players, before calmly slotting home.
Ibrahimovic scored late in the match, finishing off a counter attack.
In Mainz, German club FSV Mainz won 2-0 against Azerbaijan's Gabala FC thanks to first-half goals from Alexander Hack and Pablo De Blasis on Thursday.
Despite the win, Mainz finished third with nine points, which is not enough to progress into the round of the last 32. Gabala concludes the group stage on last place after losing all six games.
In Nice, the already eliminated from this season's Europa League, French Ligue 1 leaders Nice beat Russia's Krasnodar 2-1 to close their campaign on a positive note.
In Nicosia Cypriot champions APOEL Nicosia beat Greece's Olympiakos 2-0 at home in their Group B fixture.
The draw for the knockout stage will take place on December 12 in Nyon, Switzerland.