Kildare 1-10 Cork 0-10
Kildare finished with only 13 players but still collected their first points on a badly cut up Páirc Uí Chaoimh pitch on Sunday.
They survived the 42nd minute dismissal of Fergal Conway, who was shown a black card, having already been yellow-carded in the first-half.
Then wing-back Keith Cribbin was also black carded in injury-time with Cork substitute Brian Hurley sent off on a straight red before the end.
Kildare's goal came after 11 minutes, when Cork midfielder Ronan O'Toole slipped as he was about to challenge Jimmy Hyland.
O'Toole fouled his opponent, leaving referee Sean Lonergan with no option only to award a penalty, which Kevin Feely duly dispatched with a strong, low shot to the corner of the net.
It helped the visitors turn around after the break to play with the wind leading by 1-4 to 0-5 as Cork chalked up seven wides
Michael Hurley was the pick of the home attack, completing the scoring with a fine point after Kildare had hit three on the spin from Adam Tyrrell, Ben McCormack and Hyland from a mark.
Cork claimed three points in-a-row to be level at 0-8 to 1-5 after 41 minutes, but the introduction of Neil Flynn had the desired impact as he kicked three points to steer his side to a deserved win.
A critical moment in the tie came just after the hour, when Cork's Ruairi Deane soloed through before unleashing a powerful shot, which was deflected on to the crossbar by keeper Mark Donnellan.
Substitute Paul Kerrigan tried for a point from the rebound, but his effort veered wide at a stage when the lead was just two points.
Kildare couldn’t score in the closing 10 minutes, including the five added on, but their greater experience told as they closed out the game impressively to get back into the promotion chase.
Kildare: M Donnellan; M Dempsey, M O'Grady, D Hyland; J Murray, E Doyle, captain, K Cribbin; K Feely (1-1, 1-0 penalty), F Dowling (0-1); C Hartley, F Conway, D Slattery; A Tyrrell (0-2, 0-2 frees), B McCormack (0-2), J Hyland (0-1). Subs: A Masterson for Hartley, half-time, N Flynn (0-3, 0-1 '45) for Dowling 44 mins, C O'Donoghue for Murray 53 mins, E O'Flaherty for Tyrrell 57 mins, J Gibbons for Hyland 66 mins
Cork: M White; K O'Donovan, K Flahive, C Dennehy; J Loughrey, S Cronin, M Taylor; I Maguire, captain, R O'Toole; T Clancy, E McSweeney, M Collins (0-1, 0-1 free); M Hurley (0-5), R Deane (0-1), L Connolly (0-2, 0-1 free). Subs: P Kerrigan for McSweeney, half-time, S White (0-1) for O'Toole 48 mins, L O'Donovan for Loughrey 53 mins, B Hurley for Connolly 55 mins, K O'Hanlon for Clancy 61 mins,
Referee: S Lonergan (Tipperary)