Cussen sustained an ankle injury in a weekend challenge against Kildare at Newbridge on Saturday.
The teams agreed to play three 25-minute periods. Cork led by six points after two periods.
But the Lilywhites finished well with Tadhg Fennin hitting 1-5.
Scorers for Kildare: T Fennin (1-5, (0-3f), K Ennis, (0-3), M Hartnett, M Browne, D Flynn, E Callaghan, M Scanlon (0-1 each)
Scorers for Cork: K. O'Sullivan 0-5; M. Cussen 1-1; A. O’Connor 1-0; K. McMahon, J. Hayes, M. Harrington 0-1 each.
P. O’Shea (St. Vincent's); D. Duggan (Ilen Rovers), G. Canty, K. O’Connor; E. Sexton, G. Spillane, N. O’Leary; D. Hurley (Castlehaven), A. O’Connor (St. Colums); C. McCarthy, A. O’Sullivan (Castletownbere), K. McMahon; J. Hayes, M. Cussen, K. O’Sullivan (Ilen Rovers).
Subs: K. Murphy (Boherbue), K. O’Halloran (Bishopstown), R. O’Sullivan (Kinsale), P. O’Flynn (Ballyclough), E. Lyons (Canovee), M. Harrington (Douglas), B. Goggin (Adrigole), C. Keane (Newcestown).
E Murphy; P Cornish, D Hendy, M Scanlon; B Flanagan, M Wright, E Callaghan; W Heffernan, D Flynn; K Ennis, M Hartnett, M Browne; A Kelly, A Barry, T Fennin.
Sub: J Kavanagh for Kelly.