Ward drilled home his second goal of the night following a goalmouth scramble from a Lee Stevenson corner.
The dramatic winner arrived after the Linnets defender had cancelled out Oliver Humphries first half effort for the Yachtsmen early in the second half.
Lynn’s starting line-up showed four changes from the side that drew at Cirencester as visiting Wroxham started life under new boss David Coyle.
Wroxham took time to settle on a decent surface that became heavier as the game progressed.
The first opportunity of the night fell the way of the hosts in the 13th minute when Toby Hilliard glanced a Kurtis Revan cross over the woodwork.
Hilliard then fluffed his lines inside the box as Lynn camped in the Yachtsmen’s half during the opening 20 minutes. Revan was a constant thorn in Wroxham’s side in the opening 45 minutes as higher-level Lynn looked to stamp their authority on the tie.
Wroxham’s Craig Bussens took a heavy knock on the leg he had broken 12 months ago and the game was held up while he recovered.
The Yachtsmen took the lead five minutes before the interval when a Dan Quigley foul on the edge of the box was punished by Humphries who drilled home the resulting free-kick.
The opening goal stung Lynn into life but the Southern League outfit were unable to find an equaliser going into the break.
At half-time, Wroxham took off Matt Doyle who was replaced by Tom Rampling. Meanwhile,The Linnets were sent out early for the second half and they were soon back on level terms after Ward hammered home a Michael Clunan corner at the far post in the 49th minute.
Despite conceding, Wroxham refused to throw in the towel. The gutsy Ryman League Division One North outfit went close to regaining the lead in the 76th minute when Humphries bent another set-piece over the woodwork.
As the game looked to be heading for extra-time, some of the Wroxham players found the going becoming very tough on a heavy pitch with Jack Guyton suffering cramp to be replaced by James Baughurst.
Warburton went close to snatching a late winner before Ward did just that with literally seconds left on the clock.
Lynn: Street, Revan (Gaughran 77), Yong, Quigley, Ward, Zielonka, Clunan, McWilliams, Hilliard, Edge (Stevenson 57), Warburton. Subs not used: Setchell, McQuaid, Pearson
Wroxham: Pride, Guyton (Baughurst 84), Humphries (Mokake 87), Hastings, Lewis, Plumstead, Doyle (Rampling 46), Cook, Gilfedder, Bussens, Fowkes