The Linnets plunged back into the bottom four after losing to a wonder goal in a game where they did everything but score on Tuesday.
Bossed by midfielder Paul Raynor, long periods were spent in the Devon side's half but Lynn had little to show in the way of clear-cut chances and they hit the woodwork twice.
The visitors had two main chances - one which Steve Ovens toe-poked wide from 12 yards midway through the second half, the other which they should never have scored from.
However, Paul Chenoweth had other ideas. Deep in first half injury-time Lynn cleared a free-kick and the danger seemed over, but the Tiverton forward volleyed from the left of the box into the opposite corner.
This was hard on Lynn, who earlier meant business and had all the pressure on a dry, almost sandy pitch. Following a misunderstanding between keeper Paul Edwards and a defender on the edge of Tiverton's box, Wayne Anderson's effort was blocked.
On the quarter-hour mark Paul Watts headed onto the post a superb curling free-kick from Raynor. Glen Fuff, excellent as ever, snuffed out an away threat by blocking a Scott Rogers shot.
However, Tiverton closed Raynor down in the second half, and Lynn were not quite as effective as Tivvy indulged in time-wasting tactics and 'injuries'.
Even so, the superb David Staff had two long-range freekicks Smartly saved, while Watts wasted a good chance when latching onto keeper Steve Wilson's drop-kick.
The Walks outfit on the hour had the ball in the net, but the move had already been ruled offside.
The Linnets then used all three subs, to no avail. Two of them were involved in another move. Simon Bush - in the first team after a year's absence through work commitments and injury - laid off to Jamie Clarke, whose cross Jamie March glanced wide.
More agony came for Lynn in stoppage time as Bush's turn-and-shot was deflected for a corner, which was itself headed onto the bar by a Tiverton defender.
This leaves Lynn without a win in four home games.
Lynn: Wilson, Staff, March (Rowe 86), McNeil, Fuff, Welsh, Anderson (Bush 69), Raynor, Watts (Clarke 79), McNamara, Hayes.
Tiverton: P Ed wards, S Winter, N Saunders, S. Peters (L Vinnicombe 61), N Marker, S Rogers, K Nancekivell, S Ovens, P Everett, P Chenoweth, A Lynch (R. Peters 90). Sub not used: J. Mudge.