It looked as if the Reds were going to be held, until Scott McTominay tucked away a low shot with two minutes to go to break the deadlock.
United dominated a heavily one-sided affair in terms of possession and chances, but a heroic outing from the Cypriot side’s keeper Francis Uzoho kept them level until the death.
Erik ten Hag’s team sit second in the group with two games to go after leaders Real Sociedad won 3-0 against Sheriff Tiraspol to keep the gap at three points.
Within two minutes of United kicking off, Omonia keeper Uzoho was called into action, with the Nigeria international pushing over a curing effort forged by Marcus Rashford, following an early corner.