A LAST minute strike from Lee Stephenson spared Lynnís blushes as The Walks outfit struggled through to the next round.
Stephenson found enough space of the edge of the box before firing the ball into the far corner of the Deeping net.
It was a superb finish to an otherwise dire match, but heartbreaking on brave beeping who were just seconds away from earning a shock replay following a dogged display.
Linnets coach Darren Bloodworth, in temporary charge with manager Peter Morris away at his daughterís wedding, said: "It was a great finish from Lee and you can see why he scored a lot of goals last season.
"He took his goal well and is capable of producing something out of nothing."
Bloodworth praised the performance of Deeping, saying: "Today was their cup final and they set their stall out by getting plenty of people behind the ball.
"It wasnít a good performance from us, but we showed a lot more discipline than we did at Histon.
"I thought are back four, Lee Cowling in particular, did very well and didnít give Deeping a chance. Young Simon Nobes did very well in goal too."
It would have been a travesty had Lynn gone out, because as poor as they were, they dominated possession and created enough chances to wrap the game up earlier.
But Deeping defended in numbers and made Lynn work hard to break them down.
The closest Lynn came to breaking the deadlock in the first period was when Stephenson sidefooted wide with just the goalkeeper to beat.
Wayne Anderson and Stephenson had efforts blocked on route to goal, while Paul Raynorís corner bypassed everyone in-the Deeping box.
Lynn continued to dictate after the break. Chris Bacon fired two early efforts over the bar, while substitute Paul Watts saw an acrobatic effort just flash past the Deeping post.
A superb chip from Carl Holmes crashed against the Deeping bar in the 80th minute, before Stephenson popped up with his late winner - much to the relief of The Walks faithful.
Lynn: Nobes, Jones, Blake (Gowshall 75),. Cowling, Fuff, Anderson, Staff, Raynor, Stephenson, Bacon (Watts 54), Johnson (Holmes 45). Subs (unused): A. Weston, R. Mayes.
Deeping: J. Lowndes, R. Dell, M. Wilson, T. Korkmaz, M. Cundy, M. Goode, C. Bull, S. Woods, R. Fortune, R. Williams (D. Moseley 75), M. Drake. Subs (unused): M. Bradley, P. Reece. P. Pearson, J. Brewster.