Manchester United, hoping to avoid a winter of serious discontent, achieved a first objective by qualifying for the Europa League knockout stage amid the cold blast of sub-zero temperatures on the edge of the Black Sea.

As it transpired, Feyenoord's defeat at home to Group A winners Fenerbahce meant that even a defeat in western Ukraine would have taken United through, although a sixth successive away defeat in European competition would hardly have helped morale for the potentially difficult task as Champions League drop-outs enter the tournament in the new year.

Henrikh Mkhitaryan, slowly being integrated into the side, scored a fine first goal for the club soon after half-time, an interval in which United's players may well have felt the acid side of Jose Mourinho's tongue. The second did not come until the closing stages, Zlatan Ibrahomovic continuing his recent scoring run. Having picked a strong side, the manager might reasonably have expected more earlier on from a game of few chances at either end.

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He had insisted before kick-off that the playing surface, only passed fit, after an inspection earlier in the day was “not so bad” and “not dangerous”. It offered an easy excuse – too easy – for some of the first-half passing, which United improved after the opening goal.

They enjoyed even higher levels of possession than the 72 per cent from a 1-0 win in the first meeting, at Old Trafford in September, and apart from one early save goalkeeper Sergio Romero's most uncomfortable moment, was when a flare landed in his goal area.

Result apart, Mkhitaryan's demonstration of something like his true potential, first hinted at in the previous Europa League tie at home to Feyenoord, was the most encouraging feature. He did not sit on the left of midfield, but drifted inside in search of possession and openings, while Zlatan Ibrahimovic often came deep, trying to link up with Wayne Rooney.

United's captain was looking for the goal to equal Sir Bobby Charlton's club record of 249, but will have to wait another day after being substituted with 20 minutes left.

With Sunday's important league game against Tottenham in mind, United had left Michael Carrick at home as well as full-backs Matteo Darmian and Antonio Valencia. So there were six changes to the side that squandered two points at Everton on Sunday,with Ashley Young, a surprising choice at right-back but comfortable throughout. Eric Bailly returned after six weeks and came through well despite one heavy collision in the second half.

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Abundant possession or not, including a series of corners, there was not a United shot on target until Rooney's two just before the interval, the second of which led to a corner from which Marcos Rojo shot over the bar.

The best effort came from the home side early on, Romero pushing away a low drive by Ihor Kharatin and Ivan Petryak putting the rebound into the side-netting.

That was superseded by Mkhitaryan two minutes into the second half. He ran from the centre circle after Marcos Rojo won the ball and went on to score with a confidence that bodes well after his difficult start to a United career. The other goal, three minutes from time, was equally well taken by another summer acquisition, Ibrahmovic, who was sent clear by Paul Pogba's swivel and pass.

Zorya ( 4-4-1-1) Levchenko; Opanasenko, Sivakov, Forster, Sukhotsky; Karavayev, Kharatin (Grechyshkin, 56), Chaykovsky, Petryak; Ljubenovic (Lipartia, 71); Bezborodko (Bonaventure, 54).