Another goal from the in-form John Turner saw the Linnets battle to another win at an uncompromising Tiverton side on Saturday.
It gives Keith Webb's men a highly satisfactory ten points out of 15 as they continue their marathon early-season away programme.
The winner for Lynn came on 38 minutes as Steve Melton set up Turner to score.
Linnets boss Webb said: "It was a battling performance, and everyone played their part.
"What's pleasing is that we've gone to three places now where we didn't get any points from last year, and this year we've competed and ended up getting nine points. I'm absolutely delighted.
"They're a big, strong side. We expected a battle, and we got one. I want the players to relax a bit more, but we're becoming a lot more solid and resilient.
"We're showing we're a side that's not going to lay down and die and let teams bully us."
Tiverton, reminiscent of 1980s Wimbledon, play physical route-one football that isn't one for the purists.
Their chief plan is to bombard the box with high balls to big forward Carl Cliff-Brown, who netted the decisive goal in Tivvy's Southern League errea Cup Final success against Hemel Hempstead last season.
In the opening exchanges Cliff-Brown headed over a Luke Clark cross.
Tivvy again threatened on 15 minutes when James Palmer set up Paul Wyatt to centre for Cliff-Brown to go close with a header.
After these early problems, Lynn defended resolutely, with Mark Warren to the fore in mopping up the aerial threat, winning perhaps 80 per cent of his headers.
Cliff-Brown got booked, and was quieter thereafter.
Lynn replied with long-range efforts from Matt Nolan and Michael Frew, while Turner headed goalwards from an Adam Smith free-kick, but the ball was cleared off the line by keeper Ray Johnston at point-blank range.
But three minutes later a quick ball found Melton, who fed Turner.
The summer signing used his pace to beat two defenders and place the ball wide of the keeper. A moment of quality to lighten up a physical slog.
No doubt gee'd up during the interval, Tivvy came out and had another good ten-minute spell, after which Matt Nolan was replaced by Jack Defty, whose game was more suited to the conditions.
Defty headed wide of the left post an Adam Smith corner.
Fellow sub Danny Bloomfield also made a nuisance of himself. He fashioned a break down the left on 75 minutes, and his dangerous cross could easily have led to a goal.
The hosts tried again in the final ten minutes, but never looked like scoring as Lynn wrapped up a well-earned win.
Tiverton: Johnston, Clark (Young 73), Vinnicombe, Villis, Rudge*, T. Gardner, Martin, Palmer (Irish 73), Wyatt, Cliff-Brown*, W. Gardner*. Subs not used: Lamacraft, Gould, Wake.
Booked: Rudge, Cliff-Brown, W Gardner
Lynn: Howie, West, Lake, Warren, C. Defty, Camm, Frew, Melton, Turner (Bloomfield 68), Nolan (J. Defty 60), Smith. Not used: Fisk, Spriggs, Murray. Att: 373. Referee: P. Grenfell (Penzance).
MoM: Mark Warren.