Lynn progressed to the second round of the FA Trophy thanks to an injury time equaliser and a penalty shoot-out.
Dover made eight changes from the side that was defeated by Boreham Wood the previous Saturday with only Josh Passley, Kevin Lokko and Steven Rigg named in the starting eleven.
Lynn gave starts to Sam Kelly and Ryan Hawkins with Sonny Carey dropping to the bench and Chris Henderson out with a groin strain.
There was little to report in a rather scrappy opening. Adam Marriott and Michael Gash had early chances blocked while the visitor’s early chance fell to Joe Bedford who was well off target following a corner.
Lynn lost Michael Clunan to injury on 18 minute with Alfie Payne coming on.
Dover came a little more into the game with chances for Anthony Jeffrey and Will De Havilland but neither troubling Alex Street in the Lynn goal.
Marriott then spooned an effort over but Lynn did have the ball in the net on 34 minutes - the referee’s assistant first having his raised flag waved away by the referee but after protests from Dover the referee consulted his assistant and the goal was ruled out for offside.
Three minutes later a Dover corner found Steven Rigg whose header came back off the underside of the bar and bounced away.
Lynn took the lead on 41 minutes following nice play between Hawkins and Aaron Jones, the latter squaring the ball for Sam Kelly to smash home from 10 yards.
Two further chances fell to Lynn before the break with Rory McAuley going close with a header and Sam Kelly seeing a shot go just wide of the far post.
Lynn continued on top after the restart with Hawkins, Ross Barrows and Jordan Richards having chances blocked or cleared
On the hour Dover goalkeeper Yusuf Mersin sliced a clearance straight into the path of Gash but he hit the post with the goal at his mercy.
Dover equalised on 73 minutes when Street parried a Jeffrey centre into the path of substitute Jai Reason who chipped home.
Eight minutes later Lynn conceded again when Street failed to claim a high cross and the ball eventually found its way to Kevin Lokko to score off the inside of the post.
The game looked lost for the tiring Linnets but with five minutes of injury time played a Jones free kick from 20 yards put the game into extra time.
Extra-time failed to break the deadlock with Marriott having the best chance, his header being acrobatically clawed away by Mersin whilst Lynn ended with ten men after substitute Ryan Jarvis was injured.
Penalties followed with Jack Munns scoring the first for Dover and Marriott replying for Lynn. Rigg then missed his kick and Gash put Lynn ahead, the ball going in off the post.
Kurtis Cumberbatch then hit the post for Dover and Jones scored to put Lynn 3-1 up in the shoot out. Jeffrey made it 3-2 but Sonny Carey made sure of Lynn’s place in the next round.
Lynn: Street, Jones, Fox, Kelly (Carey 82), Barrows, McAuley, Clunan (Payne 18), Richards, Gash, Marriott, Hawkins (Jarvis 87). Unused subs: Bastock. Booked: Gash, Fox, Scorers: Kelly 41, Jones 90+5
Dover: Mersin, Passley, Lokko, De Havilland, Simpson, Bedford (Woods 85), Hinchiri (Cumberbatch 105), L’Ghoul (Munns 63), Jeffrey, Roberto (Reason 63), Rigg. Unused subs: Worgan, Rooney. Booked: L’Ghoul, De Havilland. Scorers: Reason 73. Lokko 79
Attendance: 776