After some early nervous moments, key strikers Brett McNamara and Lee Hudson were far too sharp for a ponderous Salisbury defence and set the Linnets up for a victory that was far easier than expected.
McNamara grabbed two of the goals and Hudson one to bring McNamara's total to 11 goals in nine cup games whilst Hudson has scored in every round this season.
But while these two get the headlines they will be the first to admit it was a superb all-round effort which earned the Linnets a place in the first round proper for the first time since 1984.
Salisbury, late arriving at The Walks after being delayed by M11 traffic queues, created a couple of half chances before Lynn scored, but were then quite simple blasted away.
They were down to ten men, with defender Matthew Lovell getting treatment to a cut head, when the Linnets struck twice in five minutes.
he first was a Route One goal, McNamara chasing Richard Skelly's through ball down the middle in the 32nd minute.
Salisbury should have cleared but keeper Paul Gadsby and full back Matt Parkin hesitated and that left the Lynn striker clear for a simple tap-in.
It was just a bizarre when Skelly made it 2-0, his in-swinging corner from the right somehow getting through a crowded goalmouth and into the net.
The corner had come after Hudson's stinging drive took a slight deflection and skimmed the bar. Hudson was just as close early in the second half when his shot beat Gadsby and drifted agonisingly wide of the post.
In the 70th minute he played a part in the third goal, heading on for McNamara for score superbly at the near post - and almost immediately the compliment was returned, this time Hudson finishing it off for his well-deserved goal.
And finally it was Steve Williams, whose goals had destroyed VS Rugby two weeks previously, with a close range header from Matthew Wright's cross.
Lynn: Lewis, Matthews, Skelly (Hopkins 80), Hoyle, Wright , Spearing, Pascoe,
Williams, Roberts, McNamara, Hudson. Subs: (not used) Mead, Hollman
Salisbury: Gadsby, Lovell (Sotoudeh 80), Browne, Baird, Emms, Preston, Parkin (Barham 46), Harbut, Puckett, Chalk, Rofe. Sub: (not used) McCormack)