Travel-sick Linnets' home play-off aspirations suffered a body blow with an Easter Monday defeat against another side at the wrong end of the table.
Lynn were in third place before this game.
The relegation-threatened hosts scored the only goal of the game seven minutes into the second half to leave Lynn with just two points from a possible 18 on their recent travels.
Lynn's starting line-up showed three changes from the team that defeated Hitchin on Saturday as manager Keith Webb shuffled his pack once again.
Matt Nolan returned from illness to replace the injured Jack Defty up front.
Danny Hammond came in for Mark Warren, while Jamie Gould was preferred to Mark Camm in a tactical change in midfield.
Lining up against The Walks outfit for the hosts was ex-favourite David Staff, on loan to Rugby from Conference North outfit Nuneaton.
A hard, bumpy pitch made for a scrappy start from both sides.
Despite some neat approach play, Lynn went into the half-time interval goalless, having failed to convert any of their openings.
The first opportunity went the way of Lynn in the tenth minute when some neat build up play between Nolan and Michael Frew saw the latter scrape the home post.
Seven minutes later Matt O'Halloran's snap-shot from the edge of the penalty area was gratefully caught by Farhad Afandiyev.
An early change saw Camm introduced in place of Steve Melton, who limped off for an early bath.
Lynn continued to look more likely to break the deadlock, and midway through the first period Aaron Stringfellow was on hand to head a dangerous O'Halloran centre behind for a corner.
Seconds later came a quick burst from Andrew Fisk in an opening, but the youngster dragged his effort wide.
Rugby's first chance saw David Stone volley wide after Greg Crane's clearance had cannoned off Jason Taylor into his path.
Ten minutes before the interval O'Halloran fired shy of the Rugby target.
Frew caused panic in the home defence straight after the restart, but Rugby somehow cleared their lines with a group of bodies piled into the box.
The hosts began to show more life at the start of the second half with Staff playing in more of an advanced role on the left.
Rugby took the lead in the 52nd minute when keeper Scott Howie failed to hold on to Stone's initial effort and Taylor gobbled up the opportunity to stab the ball home from close range.
The goal stung Webb's side into action, and Nolan glanced Frew's cross wide in the 55th minute.
The Walks outfit then replaced Jamie Gould with Danny Bloomfield as they looked for more of a cutting edge up front.
Nolan carved open the Rugby defence with a neat piece of skill, but the striker was denied what looked a certain goal by Afandiyev, who saved well with his body.
Midway through the half Stringfellow cleared Frew's drive off the line as The Linnets' desperation for an equaliser grew.
Another opportunity went begging in the 75th minute when Nolan failed to read Bloomfield's pass into the penalty area.
Lynn continued to pile forward, but Rugby's makeshift defence (both first-choice centre-halves were out) held firm to boost their survival hopes.
News came that Bath beat Chippenham and Team Bath beat Maidenhead, which would help Lynn out in their bid for a home play-off place.
Rugby: Afandiyev, Stringfellow, Commander, Okai, Tullin, Breward, Gearing, Francis, Taylor (Adaletown 86), Stone (Kolodynsten 78), Staff. Subs not used: Scubala, Lynn.
Lynn: Howie, West, Blois, Hammond, Crane, Fisk, O'Halloran (C. Defty 69), Melton (Camm 19), Nolan, Frew, Gould (Bloomfield 57).