That was just the first of several early openings as City continually opened up the home side but spurned every opportunity that came their way.
A neat passing move instigated by Elano and involving Robinho ended when the ball was pulled back for Ireland, who blasted wastefully over.
Wright-Phillips also tried his luck with a vicious low shot that was superby tipped wide by Georgallides.
Then came City's worst miss when, with the goal gaping, Jo took his eye off Ireland's cross and the ball span off his leg and wide.
The Brazilian did far better with City's next opening, latching on to Robinho's pass on the edge of the area and drilling a low shot against the foot of Georgallides' post.
And, before the interval, Ireland hit the woodwork again - reaching Jo's low cross but only succeeding in finding the outside of the post as he attempted to square the ball for Robinho.
Omomia's best moment of the first half had come from a cross by the impressive Dimitris Christofi that looped dangerously towards goal before dropping wide.
But, almost from nowhere, the Cypriot side took the lead four minutes after the restart.
Vincent Kompany conceded a free-kick on the edge of the area and Duro stepped up to smash an unstoppable shot past Joe Hart and into the top corner of the net.
The goal stunned City but they were quickly back in their stride and coming forward again.
Jo taps in Wright-Phillips' cross to score City's equaliser
Both Ireland and Jo continued to misfire in front of goal, however, with the former firing straight at Georgallides when clean through and Jo drilling a rasping shot against the crossbar.
It seemed a goal would never come for Hughes' side, who almost fell further behind when Hamad Ndikumana fired inches wide with a rising effort.
But Wright-Phillips was rewarded for his perseverance when he dispossessed Elias Charalambous and even Jo could not miss his eventual cross, tapping in from a yard out for his first goal for the club on 59 minutes.
Omonia were not finished yet, however, going close again when Christofi cut in from the left and crossed for Efstathios Aloneftis - whose first time effort flew narrowly wide.
By now, though, City were playing with a swagger and Jo doubled his tally on 72 minutes with a confident strike that saw him bring down Zabaleta's cross and coolly fire home with a low shot.
There was still time for Duro to send a shot crashing against Hart's crossbar from 40 yards out but City had further chances too through Micah Richards, Wright-Phillips and Ireland.
Hughes' side were almost punished again in injury time but Hart denied Clayton from close range and City held on for victory.
Manchester City boss Mark Hughes:
"Jo worked really hard for the team and I am delighted he got his reward. They were two good finishes and he will settle down now.
"It is important for a striker at a new club to get off the mark and make an impression and he did that."
"Omonia worked extremely hard and are a decent side. We knew we had to play well and there is still work to be done in the return match.
"However we are in a strong position, especially as we have away goals on the board.
"I thought we gave a professional performance in Europe and got the job done in the end."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.