ANOTHER home game, with top Conference side Farnborough, is the Linnets’ reward for an injury-time wonder goal from Adie Hayes.
They host the Hampshire side on October 27 in the fourth qualifying round.
The winners will be guaranteed £20,000 for progressing to the first round proper.
Brave Clacton were sunk following a dramatic finale, coming back from 2-0 down. But Hayes fired home a sweet right-foot shot from 30 yards.
Player-coach Tommy Wright said "It was a goal fit enough to win any game, but we shouldn’t have been in that position in the first place."
Conference high-flyers Farnborough lie eighth after winning the Ryman Premier League with ease last season and have Graham Westley as their manager and chairman.
Linnets chairman Colin Nichols said: "I’m delighted we’ve got another home draw. It will be a very difficult game, but we have home advantage so anything is possible.
"Supporters got their £6 worth on Saturday, so hopefully they’ll bring along a friend to the next round:"
Player-coach Tommy Wright said: "It’s a very tough draw. Farnborough have spent heavily in the summer and we’ll need to be at our best to go through.
The good thing is that we are at home. They won’t be relishing having to come to us and for once we will be the underdogs."
Boro won 1-0 at Telford on Saturday and have already beaten big-spending Yeovil, Stevenage and Nuneaton in the league this season.
A bumper Walks crowd was stunned when the Jewson League minnows took advantage of two errors at the back to draw level in the final minute of normal time.
There was even time for a streaker to make an entrance on the final whistle as Lynn celebrated a £10,000 payday.
Wright added: "We didn’t play as well as we did against Chelmsford, but I still thought the better side won on the day.
"We controlled the second period but their frost goal gave them a lift and panic stations set in. Clacton made it difficult for us but I knew it wasn’t going to be an easy ride:"
Both sides contributed to an entertaining first 45 minutes, which saw Lynn keeper Steve Wilson pull off one of the best saves seen at The Walks for many years.
Bobby Mayes’ 17th minute free-kick took a wicked deflection, and Wilson - diving to his right - amazingly changed momentum to his left and divert the ball round his post with the merest of fingertips.
In the 32nd minute Kristian Jones’ snapshot was well wide of the target and five minutes later Jon Whitney’s header whistled wide after a Hayes free-kick.
The opening goal came in the 40th minute when Fuff marked his 150th appearance in Lynn colours by glancing home Hayes’ corner for his first goal of the season.
Midfielder Wayne Anderson missed his third close-range sitter of the season in the 43rd minute from six yards.
Clacton, who just about shaded the first-half honours, broke up field and Shane Hillier’s dangerous cross flashed across the face of Lynn’s goal in the 45th minute, but Jimmy Clewley was unable to apply the finish.
The Linnets were largely in control after the break, but were unable to double their advantage until the 76th minute when substitute Jamie Clarke tapped home at the far post after Jamie March’s set piece had been flicked into his path by Jason Minett Clacton were still a threat, both Shane Bailey and Chris Senk striking the woodwork in a matter of seconds.
The Seasiders eventually pulled one back in the 90th minute when Wilson smashed an attempted clearance into the back of Whitney and the ball rolled into the net.
Seconds later it was all square when the Lynn defence stood still and allowed Shane Hillier to poke the ball home, despite a valiant attempt by Fuff to clear the ball as it trickled over the line.
Lynn managed to keep their composure, before Hayes’ late thunderbolt brought The Walks crowd to its feet.
Lynn: Wilson, Minett, March,Clark, Fuff, Whitney, Wright (Clarke 63), Hayes, Jones, Hudson (Evans 89) Anderson (White 88). Subs not used: Harvey and Nobes.
Clacton: Stanbridge, Cox (P. Hillier 85), S. Hillier, Hudson, Hunter, Braybrook, Howe, Bailey, -Mayes, Clewly (Farmer 80), Springett (Senk 72). Subs not used: Barder, Schultz.