Darren Bloodworth came out of retirement to help the Linnets secure an FA Cup second qualifying round tie at bogey side Bilston Town on September 27.
Bloodworth, who has continued training with the club despite quitting the game during the summer because of a knee injury, was a surprise inclusion in Lynn's depleted ranks.
He replaced ‘flu victim Colin Hoyle while Steve Lewis made his first competitive appearance since March in place of the injured James Hollman. Simon Mead also made his first start of the season with Glyn Roberts and Scott Darton on the sidelines.
Lynn were always too good for the United Counties League strugglers, but were made to work hard at times after failing to make their superiority count.
Lee Hudson broke the deadlock in first-half injury time and Lynn thought it was all over when Mead hammered home a second two minutes after the break.
But Bourne pulled a goal back and it was left to Brett McNamara to make sure of things.
Lynn dominated throughout but had to wait until the 13th minute for their first effort on goal. McNamara and home keeper Ian Flavell clashed on the corner of the penalty area and the ball looped to floodlight height before dropping narrowly wide.
Nine minutes later McNamara went even closer, this time seeing Flavell pull of a flying save to turn his 20-yard shot round the foot of the post.
A third effort from the prolific scorer saw him try to lob the keeper from the halfway line but Flavell recovered well to save under the bar.
Just as it looked as if Bourne would hold out until the break, they were caught cold from a free kick. Richard Skelly found Hudson in masses of space just outside the area and he drilled the ball home.
Flavell pulled off another good save to keep out Steve Williams' flying header 30 seconds into the second half but then gifted the Linnets a goal.
His weak clearance hit McNamara and when the ball dropped to Mead he deftly clipped it home from 30 yards.
A home substitution brought instant reward when Lee Daly saw his shot blocked and Paul Pearson blasted the rebound into the top corner.
A slip by Matthew Wright almost let in John Neal for an equaliser but his shot drifted wide of the far post.
Williams missed two good chances to increase the lead. He aimed a shot straight at Flavell and then allowed the keeper time to pull off another finger-tip save to knock the ball over the bar from point blank range.
But the final goal was not long in coming, Skelly's corner was not cleared and in the melee that followed McNamara slammed in the ball from six yards to continue his 100 per cent FA Cup scoring record for the Linnets.
Lynn withstood a late scare when Tony Spearing wrong-footed his own defence with a pass across the area but Neal's diving header went wide.
Lynn: Hollman, Matthews, Skelly, Wright (Hopkins 70), Bloodworth, Spearing, Pascoe, Mead, Williams, McNamara, Hudson. Subs ot used: Stock, Read.
Bourne: Flavell, Cooke (Clark 75), Cox, Neil, Ellis, McAllen, Sinclair (Daly 53), Wood, Neal, Pearson, Dean. Sub not used: Temple.