Erik ten Hag's men were lacklustre throughout but a special mention must go to Omonia goalkeeper Francis Uzoho, who made save after save as he almost earned the Cypriot side an incredible point.
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The Nigeria international saved Casemiro's stinging long-range strike onto the crossbar in a fairly uneventful first half.
Uzoho, who supports Man United, was on fire after the break as he made a brilliant double save to deny Antony and Marcus Rashford, before making another double save to keep out Fred's strike and an effort on the rebound from Cristiano Ronaldo.
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That then sparked a lovely moment on the pitch between Uzoho and the five-time Ballon d'Or winner, who briefly exchanged pleasantries with Ronaldo appearing to compliment his performances.
Uzoho kept out a low drive from McTominay on 81 minutes as things were looking increasingly desperate for Man United.
It wasn't all down to Uzoho, Man United lacked a killer instinct in front of goal with Rashford firing wide when played in clean through on goal, while Bruno Fernandes blazed over from close range.
And just when it looked like the home side had run out of time, Uzoho was finally beaten as McTominay slotted home from close range after controlling Jadon Sancho's cross from the left as well.
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Man United got the three points but are still three points behind group leaders Real Sociedad.
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However, this match will be remembered for Uzoho's sterling display, which deserved more than a 1-0 defeat - the 23-year-old being congratulated by the likes of Victor Lindelof and Luke Shaw as both sets of players shook hands at full time.