The hosts snatched a shock lead in the 34th minute through Karim Ansarifard, completely against the run of play.
Omonia took their 1-0 lead into the dressing room at half-time, where they were tasked with conjuring up a plan to hold out against the Premier League giants.
Man United boss Erik ten Hag didn't waste much time and summoned Marcus Rashford from the bench, who would bag the equaliser in the 53rd minute.
The game continued to go against Omonia for much of the second period, with Anthony Martial coming off the bench to put United in the lead with just over an hour on the clock.
Rashford made it a brace in the 83rd minute, slotting home an assist via Cristiano Ronaldo.
United would be given another scare, though, as Omonia responded with their second of the game 60 seconds later, through Nikolas Panagiotou.
