However, it might have been different had referee Damien Hancock not ignored what looked a foul on Ian Turner in stoppage time as he fell under a tackle by substitute left-back Philip McCabe.
Turner was the most menacing player on the park, and home manager Darius Kierans had already replaced Nathan Murphy, but McCabe fared little better against the wide right mid-fielder.
Turner’s height was a key factor in his side taking the lead in the 21st minute. He towered over the back-tracking Murphy as they challenged for a cross from Davin O’Neill into the home penalty box.
Murphy fell to the ground and Turner was left with only Peter Cherrie to beat and he duly shot home from close range.
Neither Scottish-born keeper Cherrie, making his 125th appearance for the Lilywhites, nor Cork keeper Mark McNulty, had been troubled up that point.
The goal sparked a reaction from the home side, with Paul Walsh forcing McNulty to get down well to save a low drive from the edge of the box a couple of minutes later.
Cork’s Shane Duggan joined Daryl Horgan, who was booked after three minutes, in the referee’s notebook on 27 minutes.
In the 37th minute Cork had a double let-off with Nathan Murphy’s swerving free-kick from outside the 18-yard box causing McNulty to go full stretch to turn the ball away at the foot of the post. From the resultant corner, Gary Shanahan’s header at the far post was blocked on the line.
Dundalk were lucky not to concede a second goal from a Turner free-kick.
In the second half, Dundalk started brightly. Mark Griffin darted into space in the crowded Cork box to flash a shot past the post in the 51st minute, and minutes after McNulty did well to save Walsh’s deflected shot from distance.
Dundalk caretaker boss Kierans introduced another of his new signings Lorcan Shannon and soon Dundalk were level. Gary Shanahan ran in behind the Cork defence down the left into the penalty box and shot left-footed low into the far corner.
Cork regained the impetus and were the more likely to force a winner.
Dan Murray wasted a great opportunity when he rose above the home defence only to head high and wide from Turner’s corner, while Vinny Sullivan had another header just wide.
DUNDALK: Cherrie, McLaughlin, Foran, Whelan, Murphy (McCabe 76) Walsh (Shannon59), Shields, O’Brien (McDonnell 69), Shanahan, Griffin, Rafter.
CORK CITY: McNulty, Horgan, Kevin Murray, Dan Murray, Murphy, Horgan, Duggan, Dunleavy, Turner, Sullivan (O’Connell 84), O’Neill (Kenny 72).
Referee: D. Hancock (Dublin).