Mkhitaryan's strike and a late Ibrahimovic goal separated the sides and took the PL club through in second place.
United required only a point to secure progress from Group A but Mkhitaryan's 48th-minute strike and a late Zlatan Ibrahimovic goal separated the sides and took the Premier League club through in second place behind Fenerbahce, who won 1-0 at Feyenoord thanks to a Moussa Sow effort.
The game went ahead despite concerns about the state of the icy, rock-hard pitch at the Chornomorets Stadium in Odessa, almost 1,000 kilometres away from Luhansk in the conflict-torn east of the country.
Mourinho made six changes to the United team following their 1-1 Premier League draw at Everton, including welcoming back Wayne Rooney.
After a goalless first half, United broke the deadlock three minutes into the second half as the Armenian Mkhitaryan burst forward from midfield through the middle of the Zorya defence before finishing past goalkeeper Igor Levchenko.
Sergio Romero made a good save low down from a Mikhail Sivakov header before United wrapped up the victory two minutes from the end.
A fine one-touch passing move ended with Paul Pogba sending Ibrahimovic away, the Swede running through and finishing coolly.
"I was waiting a long time for this goal. My next goal has to be at Old Trafford because I want to score at home," Mkhitaryan, who previously played in Ukraine for Shakhtar Donetsk, told BT Sport.
"The first half was a little bit difficult because we couldn't find the last pass but in the second half we created some space for the wingers and the strikers. The important thing was to win today and go through."
Earlier, a brilliant late goal by Manuel Trigueros gave Villarreal a nervy 2-1 win over Steaua Bucharest that took the Spanish club into the last 32.
Nicola Sansone gave Villarreal the lead at El Madrigal only for substitute Vlad Achim to equalise for the Romanians, who then had ex-West Bromwich Albion defender Gabriel Tamas sent off.
Villarreal won the game when Trigueros netted with a superb chip from just outside the box with two minutes left, and they go through as runners-up in Group L behind the Turkish side Osmanlispor.
Fiorentina are also through as winners of Group J after a 2-1 win over Qarabag in Azerbaijan secured by a 76th-minute goal from 19-year-old Federico Chiesa, son of ex-Italy striker Enrico. Chiesa was then sent off shortly after.
PAOK of Greece are also into next week's draw for the first knockout round thanks to a 2-0 win against Slovan Liberec, while Gent joined Shakhtar Donetsk in advancing from Group H.
Kalifa Coulibaly's stoppage-time strike clinched a 1-0 win over Konyaspor in Turkey and took the Belgians through at the expense of Braga, who lost 4-2 at home to Shakhtar.
AZ Alkmaar beat Zenit 3-2 in the Netherlands to end the Russians' perfect record in the competition and join their opponents in progressing from Group D.
Dundalk had gone into their final game in the same group away to Maccabi Tel Aviv still in with a chance of going through but a 2-1 reverse in Israel ended the Irish champions' hopes.
Romanian champions Astra drew 0-0 at home to Roma and go through with the Italians from Group E, while already-eliminated Sassuolo and Genk will try again in Group F on Friday after fog in Italy forced their encounter to be postponed.
The last two qualifying places will be decided in Thursday's later games, with Southampton requiring a draw at home to Hapoel Beer-Sheva to go through from Group K and both Standard Liege and Celta Vigo still hoping to progress in Group G.