John Caulfield's side put in a commanding performance against the Hoops, which yielded three goals, to go three points clear at the top
With the Turner's Cross crowd heaving, Cork took the lead 15 minutes into the tie after a period of frantic play between the two sides, with Billy Dennehy capitalising on poor defending to prod past Barry Murphy.
Rovers struggled to gain a foothold in the game and allowed the home side to carve out a number of chances as the half wore on. Liam Kearney tested Murphy with a rasping shot from the edge of the area just before the half-hour mark after some hard work from Garry Buckley.
Mark O'Sullivan should have doubled Cork's lead minutes later when he found himself one-on-one with Murphy but the former Avondale forward delayed his shot and was easily dispossessed by Conor Kenna.
However O'Sullivan atoned for his wastefulness when he doubled the Leesiders' advantage in the second half, heading past Murphy 10 minutes after the re-start to send the home fans into raptures.
The hosts heaped further misery on Trevor Croly's men when Darren Dennehy punished slack defending to scramble the ball over the line after the hour, making it 3-0 to Cork.
Shamrock Rovers probed in search of a goal throughout the second half but could not find a way past the stout Cork defence – a Gary McCabe free kick in the second half being the closest they got to scoring.
Trevor Croly's side never really got going and will be disappointed to cede ground in the race for the title, but victory sets Cork City up well for their trip to Limerick to contest the Munster derby on Monday.