A five-goal bonanza went the visitors' way as the home supporters went home frustrated at Terryland.
The referee let a great deal go and was far from the flavour of the month but Galway United can blame themselves in the main.
Dylan McGlade, Darragh Crowley and finally substitute Sean Kennedy continued Cork City's fine recent run on the road, with equalisers from Wilson Waweru and Killian Brouder seemingly setting United right for a victory they failed to realise through a variety of luck, poor finishing and defensive jitters.
In truth, the main reason Cork won was they had McGlade and United didn't. He's above this level.
Neither side played much in the way of passing football but it was certainly action-packed, with the hosts suffering a possibly fatal blow in their quest to catch Shelbourne.
This gives City the slightest glimmer of hope of going on an unlikely run to finish fifth.
The game ended in rain and the same pre-match, which would have reminded the 800 fans what nights here are often like, made for a really nice surface.
Cian Murphy has had a fine season and he almost made an immediate impact, hooking a cross from the lively McGlade wide.
Seven minutes in, Conor McCormack crossed and Waweru forced the veteran Mark McNulty to parry wide.
City took the lead on 15 minutes.
McGlade, who was a persistent threat and won the free-kick that led to the goal, drove low and, helped by a little deflection, it was too powerful for Conor Kearns.
McGlade's pacy run had caused the chance too.
Wawero again connected with a McCormack free-kick on 18 minutes and his header, which was going in, was tipped over by McNulty. From the corner, Brouder found the wrong side of the net.
Waweru was not to be denied indefinitely. On 24 minutes in, big Brouder's long throw was met by the local frontman and his glanced header eased beyond McNulty.
Remarkably, City were ahead two minutes later. McGlade fed Ronan Hurley whose teasing cross was fired home by Crowley.
McGlade, the best player on the pitch, again got the better of O'Keefe before his cross was prodded wide by Cian Murphy. His expression suggested as much: this was a big chance.
McNulty pulled off a truly outstanding save low down to his right five minutes before the break to deny fellow Corkonian Hurley, whose precise drive in a crowded box looked certain to make it 2-2.
Two corners later, it was level again, Brouder heading home with the aid of a bounce, McNulty scrambling like a man trying to catch confetti in the wind.
Both sides had penalty shouts, Cork's louder, in the first 15 minutes after the resumption, though it was hard to tell the merit of either in a crowded box.
It was quite feisty now on the greasy pitch.
How Keating didn't score with 20 minutes left mystified the home crowd, with McNulty blocking his all-but-open goal after he'd parried frrom the lively Shane Doherty; from the corner, Mo Nugent missed another open goal with his header.
Surely it would come?
Keating then failed to cut out a McGlade ball on 77 minutes, the Dubliner again dancing around the edge of the box, and, from Gordon Walker's cross, Kennedy slotted home sweetly. United could hardly believe it, Cork having shown very little in the second half.
Another substitute, Mikey Rowe, threatened to level matters from a close-range free only for the outstanding McNulty to parry away.
Four minutes of addition time came and went like, it seems, United's title challenge.
Galway United: Kearns; O'Keefe, Brouder, Nugent, Walsh; Hurley (Oluwa 84), McCormack, Boylan (Rowe 84); Place (Doherty 63), Waweru (Cunningham 63), Keating.
Cork City: McNulty; Walker, Coleman, Honohan, Hurley; McGlade, Byrne (Bolger 75), Crowley, Coffey, Murphy; O'Brien-Whitmarsh (Kennedy 75).
Referee: Michael Connolly.