Despite a late claim for a penalty, they did not win it at home, however, and in an irony typical of cup soccer, last night they went under to a penalty decision against them, and that ultimately cost them a place in the third-round draw.
It was hard on Galway, such was their superiority in the first game, but Damian Richardson and his players will be mighty relieved to have made it into the final 16 draw.
The initial exchanges were very tentative and it was not until the 11th minute that either managed any sort of meaningful effort on goal when Neale Fenn displayed a touch of fancy footwork on the edge of the Galway area before scuffing a weak shot wide.
Joe Gamble was next to have a pot, but having worked himself into a good position, he too failed to find the target, while Neal Horgan also made a foray forward, but his shot was also wide.
City's best early effort fell to John O'Flynn on 19 minutes after he found himself unmarked and on the end of a Roy O'Donovan cross, but Alan Gough in the Galway goal was quick to react and he saved the Cork striker's effort with his legs. City were enjoying the majority of possession and territory at this stage and beginning to assert themselves. Just before the half hour O'Flynn, running into space, was brought down by Nigel Keady, who was probably a little unlucky to get booked for the challenge. From the resultant free kick, George O'Callaghan forced Gough into a good save to push the ball over the bar.
Billy Woods then saw a fine volley dramatically headed away by Billy Cleary and then on 31 minutes, City were awarded another free on the edge of the Galway area after O'Flynn was fouled again, but O'Callaghan could only shoot weakly into the wall. There was consternation in the Galway camp when Derek O'Brien was adjudged to have made a back-pass which Gough picked up, when Fenn was the probable source, but referee Kelly gave an indirect free-kick just inside the Galway area. Danny Murphy's shot from the resultant free was well over, however.
Then, against the run of play, Galway unlocked the Cork defence to create possibly the best chance of the half. O'Brien fed a lovely through ball to Dave O'Dowd to put him clear on goal, but he screwed his shot wide.
Dan Murray was then booked for a rash and ill-timed challenge on O'Dowd and, from the free, Devine was relieved to see Fortune's free glide over after the Galway midfield duped him into expecting a cross rather than an attempt on goal. After the breakthrough, the Cork domination continued apace and Roy O'Donovan was the chief tormentor, forcing two good saves from Gough before, in the 23rd minute of the half, he was on the end of a neat Fenn lay-off and his shot was headed off the line by Frawley.
The prospect of extra-time appeared to be averted in the 25th minute of the half after Joe Gamble made a storming run down the left and his cross found O'Callaghan. However, as he wound up to shoot, Gough and Ryan contrived to bring him to the ground and the referee had no hesitation in awarding the penalty. John O'Flynn made sure of the goal with a firm shot, wide and to the goalie's right. Bad then went to worse for Galway when the combative Colin Fortune was sent off on 31 minutes. He was booked after several warnings for elbowing Joe Gamble. He did not receive the booking kindly, saying something to referee Kelly, who promptly showed him a red card.
City kept pressing, nevertheless, and both O'Flynn and O'Donovan both had good chances, while Billy Woods also went close as the clock ticked down.
CORK CITY: M. Devine; N. Horgan, A. Bennett, D. Murray, D. Murphy; B. Woods, G. O'Callaghan, J. Gamble, R. O'Donovan; N. Fenn, J. O'Flynn.
GALWAY UNITED: A. Gough; R. Frawley, B. Cleary, N. Keady, P. Reilly (Williamson, 84); D. O'Brien, C. Fortune, M. Harty, R. Casey (Moran, 70 mins); D. O'Dowd, D. Goldbey (Russell, 84 mins).
Referee: A. Kelly.