Three goals in 14 second-half minutes from Dean West, Sam McMahon and a superb one from Jack Defty meant the Linnets moved into joint second on goal difference.
It was also The Walks outfit's first win at the home of Rugby Town in their present incarnation. Results also went for them elsewhere.
An excellent all-round performance, one of the best seen away in recent seasons, meant Lynn notched their fifth win in a row.
The Linnets found space down the right flank very profitable. After three minutes Defty fired wide the first chance following a good passage of play with Shaun Carey involved.
Midway through the half the hosts' Craig Herbert had a shot cleared by Grant Cooper.
An exchange of passes between West and Cedric Anselin on the right released Matt Nolan who blazed over from six yards.
Lynn had a scare on 25 minutes when the pacy Dave Stone was denied in a one-on-one situation with keeper Aaron Benstead.
In first-half injury time Carey played a delightful ball over the top for Nolan to race onto and bring a good push over the bar by Azerbaijan under 21 stopper Farhad Afandiyev.
The second period began with the away side well on top, the best of the chances going to Matt O'Halloran, whose effort grazed the post, and Adam Smith, whose shot was deflected out by ex-Cambridge City defender Tim Wooding.
But on the hour mark came the deserved first goal. Smith sent in a corner from the right, Cooper made a nuisance of himself with the keeper, and the ball dropped to West on the floor on the goalline, who got a boot to it.
Benstead made a crucial save from a deflected shot by Wooding.
Cedric Anselin rattled the bar from 25 yards then put in Nolan, who produced a fingertip save from Afandiyev.
Anselin was involved for the second goal 20 minutes from the end, Lynn again finding the right-hand side fruitful, with Sam McMahon netting from the edge of the box via the bottom of the left hand post, the ball trickling over the line.
Shortly afterwards came Defty's sublime chip over the fast-advancing keeper after he sidestepped ex-Stamford player Andy Peaks.
Keeper John Higgs was back on the bench following his shoulder injury.
News that title rivals Salisbury and Chippenham dropped points made the day even sweeter.
Manager Tommy Taylor said: "Smithy could have got a goal near the end, trying to chip the keeper.
"They still had two chances, one from a free-kick which Aaron's made a great save from; and the other when we gave the ball away in midfield and were left short at the back.
"The full-backs were pushing up, we were trying to play as high a line as possible to help our midfield.
Rugby: Afandiyev, Tullin, Herbert, Peaks, Wooding, Byrne (Slinn 61), Gordon, Kearns, Beard (Wells 81), Stone, Evans (Thompson 87). Sub not used: Lovell. Booked: Peaks, Kearns.
Lynn: Benstead, West, Smith, McMahon, Cooper, Camm, Defty (Hammond 84), Anselin, Nolan, Carey, O'Halloran (Charles 70). Not used: Peters, Harvey, Higgs.
Goals: West 60mins, McMahon 70, Defty 74.
Referee: G. Muge (Luton). Attendance: 293. MoM: Shaun Carey.