The win, City's seventh in Dublin this season, leaves them one point in front with two rounds of games to come and the final match between the two title chasers at Turner's Cross still very much on course to provide a winner-takes-all ending to a memorable campaign.
Even the goal difference is tight at this stage with Cork's latest three points also leaving them two goals better off than the Candystripes. It may prove vital yet in this closest and increasingly unpredictable of races.
So, should Cork maintain their 100% success rate in the capital this year against Shelbourne in Tolka Park this Friday, they will go into the final game against Derry City at home with their title ambitions very much in their own hands.
In fact, win that and the title will actually be theirs if St Patrick's Athletic can defeat Derry up north on the Saturday. Unlikely, but who is to say that it won't happen?
Stephen Kenny's side have already leaked four points to Pat's this season, including a previous draw at the Brandywell, and the Inchicore side showed further evidence of their capabilities recently with their 1-0 win at Turner's Cross.
With John O'Flynn still indisposed, Damien Richardson made just the one change to the side that drew 2-2 with Waterford at the RSC on Friday evening for last night's business.
Liam Kearney has struggled somewhat in recent matches but it was still a surprise to see Billy Woods replace him on the left wing for what was the former Rovers player's first league start since way back in June.
Roddy Collins also kept his tinkering to the bare minimum with Tony Sheridan stepping into the starting XI in place of Gavin McDonnell and the 30-year old took his place up front alongside Trevor Molloy who, with a two-match suspension awaiting him, was making his last appearance of the season.
A swirling, biting wind was accompanied by a driving downpour soon after the kick off, making for difficult conditions in which to play football and, not surprisingly, it took 15 minutes for either side to fashion a goalscoring chance.
Falling, as it did, to George O'Callaghan six yards out, you would have bet your precious scarf and woolly hat that the midfielder would score, but instead he struck the leather lamely at the legs of a seemingly defenceless Barry Murphy in the Rovers goal.
Midway through the half though the wind began to change direction and bear down on Michael Devine's goal. So too did Rovers. First Marc Kenny flipped over a free kick from 20 yards straight into Devine's mitts and then full-back Keith Doyle saw a 25-yarder cannon off a Cork torso and out for a corner.
Cork responded in kind as the wind began to die down and only the late intervention of Brian Shelley's boot stopped the superb Joe Gamble from sticking Murphy's inswinging free-kick into the rigging.
Rovers struck back less than two minutes later, Kenny firing in a vicious 25-yard effort that zipped off the surface before Devine somewhat fortunately gloved it onto the post and back into his arms.
By now it seemed to be a toss of a coin as to who would break the deadlock and O'Callaghan had two half-chances thwarted in rapid succession ten minutes before the break before the opener finally arrived.
Talk about a gem too. Gamble started it by twisting through a thicket of snapping Rovers tackles inside the centre circle before releasing Neale Fenn 10 yards out from the Rovers area. Fenn spotted Roy O'Donovan wide on the left and both ball and run were timed to perfection with the City forward poking the ball under the advancing Murphy and over the line.
Cork proceeded to turn the screw after the interval and with over half an hour to play the result was a done deal with the visitors 2-0 up and the hosts down a man. The goal came first and it was another beauty.
Rovers defender Kieran Foley gave away possession and O'Donovan's slide rule pass across the box was dummied by Fenn which allowed Gamble time to slip the ball past Murphy.
Two minutes later Foley's night got a whole lot worse when he was harshly shown a straight red card for a late tackle on O'Donovan in the centre circle and it was game, set and match if not championship.
Rovers, mindful of their own precarious league position no doubt, battled on gamely but any attempts to salvage something from the wreckage was torpedoed after 77 minutes when Hugh Whoriskey again sent off a Rovers man harshly. This time it was Marc Kenny who made for the line after an accidental elbow on O'Brien.
CORK CITY: M Devine, N Horgan, A Bennett, D Murray, D Murphy, J Gamble, C O'Brien, G O'Callaghan, B Woods, N Fenn (Behan 88), R O'Donovan.
SHAMROCK ROVERS: B Murphy, B Shelley, K Doyle, W McDonagh (I Ryan 79), K Foley, D Tracey (R Manley 65), M Kenny, L Roche, M Rutherford, T Sheridan (C O'Connor 61), T Molloy..
Referee: H Whoriskey (Dublin).