The one-off clash with Dr Martens League Western Division champions Redditch proved one game too many for Darren Bloodworth and Kevin Boon's troops, who will have to be content with a place in the Dr Martens Premier Division next season.
A second half strike separated the two sides to leave The Linnets' title-winning weekend in heartache.
Lynn made one change from the side that clinched the Eastern Division title at Fisher on Saturday, with Mark Heath-Preston replacing Mark Burrows on the bench.
Before the kick-off The Walks outfit presented recently departed midfielder Paul Raynor with his league winner's medal on the centre circle.
Somehow a breathtaking first half ended 0-0.
The Worcestershire side were the first to threaten, and twice in the space of a minute Steve Wilson made two sharp reflex stops to deny headers from Gary Knight.
Five minutes later Carl Holmes picked out Mark Camm in space, but the midfielder's effort was well wide.
The Western Division winners continued to hold the upper hand, and Wilson foiled Alex Cowley with his legs before Knight's goalbound header was turned over the bar by Richard Leadbeater from the resulting corner.
An end-to-end encounter saw David Staff conjure up some magic on the right and Matt Gardiner was forced to turn the ball behind with Dale Watkins waiting to pounce on 18 minutes.
Midway through the half a mix-up between Neil Manton and keeper Richard Anstiss nearly gifted Lynn the opener, but Holmes failed to capitalise on the visitors' first mistake of the match.
Lynn were beginning to grow in confidence after weathering the early storm, and 15 minutes before the break Staff burst through the rearguard following a pinpoint pass from Lee Stevenson, only to fire over.
A delightful move saw Lynn breach the Reds' defence again in the 35th minute when Camm headed Staff's delivery inches over the woodwork.
The large crowd had a slight pause for breath before, on the stroke of half-time, Wilson pulled off an awesome double save.
In first half stoppage time a free-kick looped over the head of Danny Hammond as the defender looked set to nod home.
Both sides made a change for the start of the second period, Chris Bacon coming on for Watkins while the Reds swapped full-back Manton with Quentin Townsend.
After a quiet opening, the deadlock was eventually broken in the 56th minute when Burgess sprinted on to a long ball over the top before blasting past the helpless Wilson.
Lynn's response was swift with a Staff free-kick testing Anstiss to his right.
The Linnets enjoyed plenty of possession but were lacking a cutting edge in the final third of the field.
Fifteen minutes from the end Leadbetter was denied by the brilliance of Wilson before firing the loose rebound wide in a golden opportunity to put the game out of reach.
Staff looked the most likely player to pull an equaliser out of the bag, and in the 83rd minute his half-volley whistled past Anstiss's right post.
Both teams left the field to a standing ovation, and quite rightly so after the travesty of such a play-off taking place.
Thus Redditch on Saturday travel to the 14th-placed side in the Dr Martens Premier, Merthyr Tydfil, for the right to be promoted to the new Conference Two division next season.
Joint boss Darren Bloodworth said: "We've won the league, the players haven't been able to celebrate, and we've been kicked in the teeth by having to play this play-off.
"The lads' heads are on the floor in the dressing-room, and the players deserve better than that after such a good season.
"Looking at the game, we didn't play as well as we could and we found Redditch hard to break down.
"They weren't the best side we've played this season, but they weren't the worst either."
Lynn: Wilson, Jones, Defty (Heath-Preston 83), Hammond, Fuff, Stevenson, Woodrow (Harris 65), Holmes, Staff, Watkins (Bacon h-t), Camm. Subs not used: Fishlock, Nobes.
Redditch: Anstiss, Manton (Townsend h-t), Gardiner, Taylor, Knight, Myers, Hall (Softley 60), Scheppel, Leadbeater, Burgess (Shepherd 79), Cowley. Subs not used: Voice, Woodley.
Goal: Burgess 56.
Referee: M. Bull (Essex).