Manchester United huffed and puffed but needed 92 minutes and a goal from Scott McTominay to breach the Omonia goal after having more than 30 attempts at Old Trafford.
The underdogs caused the Red Devils problems last week before eventually losing 3-2. They kept things much tighter in the return fixture, though, and almost frustrated their heavyweight opponents, who thought they were set for an embarrassing stalemate.
Francis Uzoho, Omonia's Nigerian goalkeeper, who himself is a fan of the Red Devils, was in inspired form as he continued to deny the home side with United's winner coming from an unlikely source in McTominay, who scored only his second ever goal in Europe.