Kildare finished the stronger to claim the points at Newbridge. Wexford had the more promising start and led for a time in the opening half but their failure to convert enough scoring opportunities in the second half cost them a possible share of the spoils.
The Slaneysiders travelled to Newbridge with some optimism and corner-forward Matty Forde, who finished as the game's top scorer and full forward John Hegarty caused many problems for Kildare.
Matty Forde converted two Wexford frees in the opening four minutes and although Kildare drew level in the 20th minute through Kenny Duane they quickly fell behind again.
Matty Forde punched a high lop from Hegarty to the Kildare net in the 24th minute.
Kildare's recovery began with a Tadgh Fennin point and three more followed without reply to leave the sides tied at 0-8 to 1-5 at the interval.
Wexford were playing quite well but when they allowed Kildare to build-up a lead after the restart they were unable to find their way back. John Doyle pointed twice and Michael Ryan also scored without reply for Kildare.
Brian Murphy, introduced at the start of the second half, grabbed a late goal for Kildare to put the result beyond doubt.
KILDARE: E Murphy; K Doyle, R Quinn, J Bracken; K Duane (0-2), Martin Ryan, A Rain- bow (0-1); K Brennan, Dermot Earley; P Murray, J Doyle (0-4, 3 frees), Michael Ryan (0-1); P Brennan (0-2, 1 free), David Earley, T Fennin (0-3, 2 frees). Subs: B Murphy (1-0) for Murray, A McHugh for P Brennan, E McCormack for David Earley, J Gilroy for Michael Ryan.
WEXFORD: O Murphy; C Morris, P Wallace, M Gahan; D Murphy, D Breen, L O'Brien; J Berry, I Wickham; R Barry, M Mahon, T Howlin; P Forde, J Hegarty (0-2), M Forde (1-6, 4 free). Subs: D Kinsella for Wickham, J Lawlor for Mahon, E Galavan for Barry.
Referee: R Doone (Antrim).