Having laboured to unimpressive wins against EB Streymur in the first qualifying round in July, the Blues needed penalties before seeing off FC Midjtylland to reach the first round proper.
And Mark Hughes' men were forced to come from behind to secure a narrow win in Cyprus against a side that finished 3rd in their domestic league last season.
Hughes opted to start with Jo, Shaun Wright-Phillips, Robinho and Elano, and although they spurned several opportunities to give City a bigger advantage for the return leg, the home side also had chances of their own.
City's £32.5million Brazilian Robinho almost netted after only two minutes when his fierce shot was parried by Omonia goalkeeper Antonis Georgallides.
Stephen Ireland and Wright-Phillips also went close to breaking the deadlock in the opening stages but it was Jo who wasted the clearest first-half chance in the 27th minute.
Ireland squared the ball to the Brazilian who somehow managed to slice the ball wide with the goal gaping.
Thirteen minutes later Jo's shot hit the post and, just before the break, Ireland's effort also came back off the woodwork.
After dominating the first period, City were shocked to fall behind early in the second half when Klodian Duro's superb free-kick beat Joe Hart.
After Ireland had wasted another excellent chance, City finally equalised when Jo turned home Wright-Phillips' pinpoint cross.
After 72 minutes Jo was on target again as he gave City the lead after showing good skill to control Pablo Zabaleta's cross before firing his low shot home.
Omonia almost hit back immediately when Klodian Duor's long-range effort came back off the crossbar with Hart beaten.
However, City deserved their victory which should have been comprehensive but for some wayward finishing.