In-demand striker Matt Nolan was on target twice as the Linnets extended their unbeaten run to 10 matches in Devon with their sixth straight win.
Nolan, a target for AFC Wimbledon early last week, bagged a goal in each half as Lynn moved back up to second in what is proving to be a enthralling title race.
The Dons' bid for Nolan, who has already scored double figures for Lynn since joining around Christmas, has gained the attention of BBC East regional television.
With Bath City maintaining top spot by beating Northwood, the championship destination is beginning to look a three-horse race between Lynn, Bath and Salisbury, both who Lynn host in the final month of the season.
But third-placed Chippenham still have a glimmer of hope with a fixture at Bath, who also have to entertain Salisbury, whose fixture backlog seems to have taken its toll in recent weeks.
Lynn boss Tommy Taylor, who remains adamant that if his side win their last eight games then the title will be theirs, said: "It was a hard win, especially in the second half.
"We missed some chances that we usually take and that put some pressure on us.
"Other than a couple of crosses Tiverton didn't have a chance in the first half and in the end I was disappointed that we conceded a goal.
"The boys in midfield worked their socks off. We just need to pass it a bit better.
"We were the better side and it was another game where the result was far more important than the performance."
Lynn took the lead on nine minutes when a defence-splitting pass from Adam Smith found
Nolan in space and the striker gave former Wisbech keeper Mark Ovendale, on the receiving end of some customary taunts from the Lynn fans, no chance.
There was little action in the first half - the home side possibly edging possession but Lynn's defence were rarely troubled other than a couple of crosses into the box.
Tiverton continued to apply pressure in the second half but poor defending saw The Walks outfit increase their lead on 51 minutes - McMahon finding
Nolan to find the back of the net from 12 yards.
Tiverton should have got back into the game on 64 minutes but Booth shot over when well placed and soon after McConnell somehow managed to direct his header wide.
Lynn midfielder Jack Defty had a long range effort off target and Nolan hit the upright.
Tiverton's Chris Holloway reduced the arrears with four minutes remaining when he was on hand to force home after Aaron Benstead had dropped a routine centre. This set up a tense finish, but battling Lynn held on for another crucial three points.
Tiverton: Ovendale, Booth (Hambly), Davies, Gould, Croft (Beddow), Milsom, Ampadu, Bale, McConnell, Holloway, Mudge. Subs not used: Nogan, Skinner, Kelly.
Booked: Gould (14mins), Holloway 27, Croft 45. Goal: Holloway 86.
Lynn: Benstead, West, Smith, McMahon, Cooper, Camm, Defty (Hammond 84), Anselin, Nolan, Carey, O'Halloran (Charles 64). Not used: Peters, Harvey, Higgs.
Booked: Cooper 80. Goals: Nolan 9, 51. Referee: P. Grenfell (Penzance). Att: 351.