A poor fisted clearance by Conlon in the sixth minute fell to Kevin Rowe minute but the netminder upended him in the box and Gary Sheehan made no mistake with the spot-kick.
Although Town enjoyed the majority of the possession in the first half they failed to create too many goalscoring opportunities. John Lester headed Ryan McEvoy’s corner over in the 12th minute. Right on the stroke of half-time Lester’s free was superbly tipped over by Youths keeper Pakie Holden.
Youths were happy to soak up the pressure with David Breen blazing over a 20-yard drive in the 15th minute.
Another rush of blood from Conlon in the 61st minute nearly led to the visitors doubling their advantage but defender Niall O’Reilly was on the line to clear Danny Furlong’s effort.
Town pressed hard an equaliser with Peter Hynes, McEvoy and Mark Salmon all coming close with efforts.
LONGFORD: Conlon, O’Reilly, Byrne, Kelly (Hyland 66),K Cronin, McArdle (Glynn HT), Lester, Salmon, McEvoy (G Cronin 74), Hynes, Freeman.
WEXFORD: Holden, Wolfe, Russell, Breen, Broaders, Byrne(Kehoe 90), Malone, Keohane, Rowe (Mullen 86), Sheehan, D Furlong
Referee: J Grimes (Dublin)