These two sides remain unbeaten in the eircom League of Ireland Premier Division after a Tolka Park encounter that was defined by two goals just before half time.
Cork City went in front in the 44th minute after Joe Gamble picked out George O'Callaghan, whose effort from the middle of the box crept over the goal-line.
Shamrock Rovers drew level before the break, with captain Stephen Rice latching onto a Sean O'Connor free-kick to volley home.
Dessie Baker almost won it for the hosts at the death, but his shot was well saved by Cork stopper Michael Devine.
The travelling fans made their presence felt even before kick-off, with a cloud of green smoke shrouding the chilly Drumcondra venue.
It soon cleared, although the crowd wouldn't have missed anything in an opening 15 minutes that failed to produce a chance of note, with both sides looking comfortable up until the final third.
The game sparked to life in the 16th minute when Devine almost gifted an opener to Rovers. The netminder made a mess of a back-pass, but recovered quickly enough to twice prevent Baker from putting the Hoops in front.
Devine's counterpart Barry Murphy was called into action five minutes later when he came from his line to tip the ball off the head of the incoming Cillian Lordan.
City's passing was much slicker than their opponents, but it took until a minute before the break for it to pay dividends. Gamble and Liam Kearney worked a neat one-two and the former got to the by-line before cutting the ball back to O'Callaghan near the penalty spot.
The enigmatic number 10's first touch was poor but his placed shot scrambled over the line despite the best efforts of Devine and a couple of his defenders.
O'Callaghan, who had received a hostile reception from the home supporters, was quick to let them know that it was he who had put their side behind.
The Cork celebrations were short-lived, however, as within two minutes the hosts were back on terms.
O'Connor's quickly-taken free caught the Rebels' defence napping and Rice, who was the man-of-the-match in Rovers' opening day win over Drogheda United, clinically steered his volley past the helpless Devine.
The visitors had a half chance five minutes after the restart when a pass from O'Callaghan found Colin Healy in space on the edge of the area. Unfortunately for Alan Mathews' side, the former Sunderland midfielder dragged his shot wide of he left upright.
Rovers had a decent opportunity on the hour mark. A beautifully-weighted through ball from Ger O'Brien was almost controlled by Baker, and substitute Eoin Doyle was on to the loose ball in an instant to flash a curling left-footed shot just over the crossbar.
Cork skipper Gamble almost followed his counterpart onto the scoresheet, but his thunderous 20-yard drive was too high and just wide.
Devine then showed speed and bravery when saving at the feet of Eric McGill after the Rovers winger raced onto a delightful ball by Doyle. McGill tested Devine again after 75 minutes, but the 'keeper was fortunate the shot from distance came straight at him.
Danny Murphy should have given Cork the lead soon after when the full-back made a storming run into the box only to slice an effort off his left boot.
Baker came close to snatching the points two minutes into injury time. The striker pounced on a mistake by centre-back Dave Mulcahy but Devine, at full stretch, tipped the ball past the post.
Shamrock Rovers: B Murphy; O’Brien, Maguire, Ferguson, Flynn; McGill, D O’Connor, Rice (c), S O’Connor (Martin, 80 mins); A Murphy (Doyle, 58), Baker.
Cork City: Devine; Sullivan, Mulcahy, Lordan, Murphy; O’Callaghan, Gamble (c), Healy, Kearney; Mooney (O’Flynn, 90 mins), Behan.
Referee: T Connolly.
