Ruairi Keating's late goal finally broke eight-man Shamrock Rovers’ resistance on an extraordinary night at Turner’s Cross.
Richie Towell, Johnny Kenny and Sean Hoare were all sent off in a flurry of red cards, as the Hoops fell to back-to-back defeats and City, for the first time this season, recorded consecutive wins.
Any hope of a Rovers fightback - after last weekend’s shock home defeat to Drogheda United - were extinguished inside a few crazy second-half minutes.
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Kenny saw red within four minutes of his arrival and Hoare followed him down the tunnel moments later.
That was the signal for Cork - one of only two teams behind Drogheda at kick-off - to push on for the win.
They got there in the end, but didn’t gain any ground on Drogheda, who also picked up three points.
As for Rovers, it’s another dent to their four-in-a-row bid as Derry City, a point clear at the top, can extend their lead tonight against struggling Sligo Rovers.
The drama kicked off shortly before the break as Keating headed a Barry Coffey corner wide of the target.
Attention quickly switched to the back post, where Cork’s Gordon Walker and Rovers’ Towell were lying next to each other on the turf.
After some confusion, referee Sean Grant consulted with his linesman, returned to the six-yard box and showed a straight red card to the Hoops midfielder.
While replays failed to clear up what exactly happened as Towell and Walker came together, the ball was still in play when the incident occurred.
Yet Grant signalled for a goal-kick and not a penalty, and Keating seemed to be the only Cork player to plead the case for a spot-kick.
Towell’s departure was a huge blow for the Hoops, as he looked to be their liveliest attacking option in a largely frustrating first-half for the champions.
He tried his luck from distance on a handful of occasions, but couldn’t find the target.
And just minutes before his sending off a heavy touch inside the area robbed him of Rovers’ best chance of the opening period.
Markus Poom pierced the City back-line with a fine through-ball, Towell took it on the turn, but failed to control the ball, and that allowed goalkeeper Jimmy Corcoran an opportunity to narrow the angle and make a point-blank save.
There were some other half-chances for the visitors. Gary O’Neill twice sent headers from Jack Byrne corners high over the bar.
Estonia international Markus Poom fired narrowly over from the edge of the area and O’Neill failed to keep down his 20-yard effort after controlling Darragh Crowley’s clearance.
Having regrouped at half-time, Cork set about after the break at trying to make their one-man advantage count.
Keating fired a tame shot at Leon Pohls from 20 yards while an unmarked Gordon Walker was screaming for a switch to the right.
And after a Coffey free-kick pinballed around the area, Walker wasn’t far away with a clever lob.
But there was no doubting who the main man was last night.
All eyes turned to referee Grant as he sent off two Shamrock Rovers players - both for two bookable offences - inside an extraordinary seven-minute period.
Kenny was barely 20 seconds on the pitch when he was booked, seemingly for something he said to the assistant referee.
Four minutes later and the on-loan Celtic striker was shown a second yellow and then a red card for a foul on Josh Honohan.
Another two minutes passed and centre-half Hoare was booked for dissent. Within a minute of that, Hoare was given his marching orders for a high challenge on Coffey.
Hoops boss Stephen Bradley replaced Farrugia shortly after that with Ronan Finn, before the wing-back, who was also on a yellow, could get himself into trouble again.
Three men to the good, the Leesiders pushed on for a win that even the most optimistic of fans would not have believed likely before kick-off.
However, Rovers set themselves up to squeeze the space in their final third and they made it difficult for the Leesiders to create too many chances of note.
Keating headed one over on 73 minutes and Tunde Owolabi’s heavy touch meant he could not capitalise on Aaron Bolger’s low centre.
At the other end, meanwhile, Rovers substitute Darragh Nugent was inches off target with a header.
City finally went in front on 85 minutes when Kevin Custovic raced down the right and crossed towards the back post, where Keating produced an emphatic left-footed finish.
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