United secured their place in the last 32 of the Europa League after a dominant victory in freezing conditions in Odessa.
The visitors only needed a point against already eliminated Zorya but a wonderful goal from Henrikh Mkhitaryan - his first for the club - set us on our way and the win was sealed late on through Zlatan's 13th of the season.
Fenerbahce won 1-0 at Feyenoord in the other game to ensure their place in Monday's draw as group winners, one point ahead of the Reds.
United will be unseeded in the last 32 and will play the first leg of the tie at home as a result, but four wins from six games represents a fruitful return from what was one of the tougher groups.
Despite the fact they were already out, the hosts started well and went close twice early on.
Sergio Romero saved well to repel Ihor Kharatin's 25-yarder and then Ivan Petriak fired his follow-up into the side netting on the angle.
Paul Pogba flashed a shot over the bar and then headed narrowly wide, before a flurry of United chances shortly before the break.
Eric Bailly was superb on his return after six weeks out and went close with an acrobatic effort, Igor Levchenko saved well from Wayne Rooney and, from the resultant corner, Marcos Rojo blasted off target from close range.
United continued to press and the breakthrough arrived three minutes after the interval as Mkhitaryan opened his Reds account in supreme style.
He collected the ball on halfway and waltzed through the Zorya defence, shimmying away from one player, nutmegging another before he calmly slotted the ball beyond the advancing keeper.
Zorya, to their credit, continued to try and get themselves back in the tie but United's defence, and Bailly in particular, stood firm and the hosts rarely threatened.
Romero saved smartly from a Mikhail Sivakov header from close range but that was as good as it got.
Substitute Marouane Fellaini, who this time caused problems in the opposition box, went close and Ibra fired an effort over the bar from distance as the Reds looked to kill the game off.
We did so in the dying seconds when Pogba's superb clipped pass picked out the Swede, who raced clear and slotted home beyond Levchenko for his seventh goal in as many games.
Overall team performance: 8/10
United Faithful Man of the Match: Eric Bailly was excellent on his return, but Henrikh Mkhitaryan gets MOTM again this week for another superb showing. Oozed class and quality.