Zlatan Ibrahimovic scored the only goal in the second half to give Manchester United victory over Ukrainian side Zorya Luhansk.
The Swede struck on 69 minutes, rising highest at the back post to power home a header from close range after Wayne Rooney had miscued a shot.
United were far from at their best, and with two-thirds of the game gone they had yet to record a shot on target as the visitors from Ukraine proved tough to break down.
Fenerbahce’s win over Feyenoord means that Jose Mourinho’s men sit second in the group, and they play the Turkish outfit next in three weeks time.
Two weeks on from opening their maiden group stage campaign in the competition with defeat at Feyenoord, Jose Mourinho conceded his side could ill afford to falter against Thursday’s relatively unknown Ukrainian opponents.
Zorya certainly played their part at Old Trafford and frustrated the hosts for large parts, but Ibrahimovic’s close-range header would eventually secure a 1-0 win that may not have enthralled but kick-starts United’s Group A campaign.
Mourinho’s side dominated possession from the outset but struggled to translate that control into goals, unlike Saturday’s shellacking of reigning Premier League champions Leicester.
United scored three goals from corners that day and their best first-half chance came via the same route, with Marcus Rashford’s thumping effort hitting the underside of the crossbar.
Zorya were proving a nuisance on the break but struggling to threaten Sergio Romero’s goal, with United snatching a winner two minutes after Wayne Rooney came off the bench.
The England captain’s mishit effort was headed home by Ibrahimovic, securing an important three points from an uninspiring match.
The big talk pre-match was captain Rooney’s place among the substitutes for a second successive match, watching from the dugout as his team-mates struggled for consistency in a tame opening.
Zorya boasted nowhere near the same talent but did not appear overawed by the stage, looking particularly threatening on the counter-attack.
The hosts came closer still moments later. Juan Mata’s corner was flicked on by Paul Pogba into the path of Rashford, who met the loose ball with a rasping right-footed strike that rattled the crossbar but crashed down just in front of the goal line.
It was the closest United came to a first-half opener as Zorya broke up the play, leading to a testy exchange between Mourinho and counterpart Yuriy Vernydub.
The Red Devils’ lack of goals was not for the want of trying, though. Ibrahimovic, Mata, Jesse Lingard and Marouane Fellaini tried their luck, while a timely intervention prevented Ibrahimovic easily directing home.
Half-time allowed the Ukrainian visitors to settle and they returned strongly, with Olexandr Karavaev’s fine cross just evading Zeljko Ljubenovic.
United’s own attempts to create an opening down the flanks were coming to nothing, leading to Rooney’s introduction shortly after Zorya substitute Paulinho got away a curling effort from the edge of the box that a diving Romero palmed away.
The 67th-minute introduction was followed by a goal within two minutes, leaving those around Old Trafford breathing a sigh of relief.
Neat play down the right ended with Timothy Fosu-Mensah pulling back for Rooney. While the substitute could only hit his effort into the ground, it threw Zorya’s goalkeeper off-balance and Ibrahimovic rose to power home a close-range header.
It proved the decisive moment of a turgid tie.
Mikhail Sivakov impressively cleared an Ibrahimovic cross off the line unaware offside had been called, before Fellaini missed the target and Karavaev had an attempt at goal stopped by Romero.
Zorya goalkeeper Oleksii Shevchenko got down to prevent an Ibrahimovic free-kick creeping in, but there was to be no second goal to celebrate