A magnificent win, despite the Linnets going behind in the second minute, missing a penalty and playing the last 35 minutes with ten men.
This ensured Lynn notched their third win at Cheriton Road in two seasons (remember Lyndon Rowland's FA Trophy hat-trick?). It sets them in good spirits for Saturday's Trophy trip to Conference high-flyers Morecambe.
Matty Clements was given a straight red card for dissent.
Referee Mr John confirmed it was for foul and abusive language over a disputed decision.
On target were on-loan Norwich City striker Danny Bloomfield his seventh goal in nine games and defender Simon Dakin.
"We were magnificent," said Lynn manager Tony Spearing.
"We've had a moan at Dakes that recently he hadn't been scoring enough, and he's been outstanding the last two games."
The Linnets had to recover from a setback in the first 90 seconds. Nicky Dent's long-range effort hit the base of Steve Wilson's right-hand post and it fell nicely for Anthony Henry to convert the rebound put the hosts ahead.
But the visitors picked themselves up and proceeded to dominate possession and territory. Only a frequent wrong option on the final ball prevented them from scoring.
Even so, chances were there.
Clements went on a determined 60-yard run and was only denied by a last-ditch tackle.
From a clever flick-on by Zeke Rowe he shot just past the angle of post and bar, and then after more good work by Rowe and Jason Minett he should have done better with a free header than place it wide.
Danny Bloomfield had two efforts blocked in a matter of seconds. Both sides could have had penalties before Lynn were awarded one in the 18th minute when Dan Larkin pulled back Rowe.
Adie Hayes spot-kick was hard to David Wietecha's left, but the giant keeper pulled off a good save.
Three minutes into first half stoppage time Bloomfield got an opportunistic equaliser, striking home a close-range left foot volley following a Rowe flick-on from a corner.
The first incident of the second half was Clements sending-off on 55 minutes, for protesting after it appeared Bloomfield had earned a corner when the decision was a goal-kick.
Following instructions from his assistant the referee gave Clements, another on-loan forward, his marching orders.
On the hour came one of Folkestone's few chances, starting from their most dangerous player, full-back James Virgo. But the alert Jamie March stopped James Dryden's effort on the line.
Five minutes later came The Walks outfit's deserved winner, again from a corner.
Dakin nodded home to prompt his corner-flag celebration slide, which turned out more like a belly-flop.
Invicta hit back and put pressure on with a succession of corners, as they were bound to do with an extra man. But Lynn resisted with Glen Fuff, March and the outstanding Dakin to the fore.
And there was no better man than Rowe to play "keep-ball" at the other end. If his ball-holding skills were paired with Bloomfield's scoring instincts and pace, Lynn would have the perfect striker.
Even more impressive was that the ten men did not need a substitution until the final minute.
Folkestone: Wietech, A Morris, Virgo, A Larkin, D Larkin, A Hogg (Ayling), Chandler (Azzopardi 86), Bower, Dryden, Dent, Henry. Sub (not used) Daniels
Lynn: Wilson, Dakin, March, Minett, Fuff, White, Anderson, Hayes, Bloomfield (Hudson 90), Clements, Rowe. Subs: Evans, Suiter.
Sent Off: Clements (55 dissent) MoM: Simon Dakin Att: 382