Danny Bloomfield notched up Lynn's fourth penalty miss in six games as Lynn drew a blank with the Ridgeons League side.
Linnets boss Keith Webb said: "Frustrated – yes, but worried – no, about not putting the ball in the net in tricky conditions.
"It's something we said about last season, and I think we're ahead of where we were last season. The passing is better and we opened them up.
"I can't remember Rob Murray having a save to make.
"They put everyone behind the ball and it was a moral victory for them."
Michael Frew and John Turner hit the bar within the first quarter-hour.
Turner, Bloomfield and Greg Crane all had first half chances, while ex-Lynn striker trialist Stewart Roach blazed over for Yarmouth Town.
Lynn dominated the second half, and early on Joe Francis was fouled by Yarmouth sub Tom Godbold, but home keeper Elliot Pride saved well from Bloomfield's low penalty.
Francis missed from the spot at Gloucester and Merthyr in the final two games of last season's BGB League-winning campaign, while Ben Sedgemore hit the post with his spot-kick last week against Clyde.
Mark Peters, recovering from a groin strain, came on and was one of the players to head over from a succession of late Lynn corners.
|Great Yarmouth: Pride, Watts, Lee, Smith, Palmer, Darby, Lamb, Sullivan, Roach, Bartley, Crawley. Subs (all used): Godbold, Woodcock, Hackney, Savage, Vide, Lawrence.
Lynn: Murray, C. Defty (Peters 66), Chapman, Weaver, Crane, Turner (Kelly 68), Fisk (Bridgwater 63), Camm (Sedgemore 63), Bloomfield (J. Defty 58), Frew (Joachim 58), Francis. Sub not used: Howie.
Referee: L. Betts (Norfolk). Attendance: 180.