DEFENDER Mark Burrows and Lee Stephenson's fourth goal in three games sent the Linnets through as they gained revenge for an FA Trophy exit by the Daniels.
All three goals came from headers, and one in each half ensured Lynn progressed to the last 16.
Because the sides met on Tuesday for the fourth time in 11 weeks it was a scrappy game, with each side familiar with the other's play.
Lynn boss Peter Morris said: "Although we've played a lot better over the last month it's important to get results when we're not playing as well.
"One of the biggest plus points was Lewis Blois getting through 45 minutes.
"Although below par, collectively we're improving as a team"
Lynn attacked from the start, and Stephenson forced a block from keeper Darren Horrigan, who then needed to save Carl Holmes' stinging effort at the second attempt on the quarter-hour mark.
With neither side's passing up to scratch, there were few opportunities in the remainder of the half, with Stamford not managing a shot on target.
However, Stephenson woke up proceedings a minute before the break with his 14th strike of the season, guiding home at the far-post a typically dangerous David Staff cross.
Blois came on at halftime, back for the first time since August's injury. The Daniels' substitution came to more dramatic effect.
Within two minutes of coming on, Gareth Pritchard took advantage of good work by Malcolm Ndekwe to stretch the home defence, and centred for Kevin Byrne to head the equaliser on 52 minutes.
Holmes headed wide a deep Paul Raynor free-kick, but on the hour Burrows did better by nodding a looping effort over the keeper and a despairing defender after Staff was fouled on the right touchline.
Just after coming off the bench Chris Bacon should have done better when well placed, but shot wide.
Stamford's best chance of the game came in the last minute after a quick freekick when Richard Thompson shot across goal from the right of the box.
Lynn: Greygoose, Jones, Cowling (Blois h-t), Burrows, Fuff, Defty, Weston, Raynor, Stephenson (Bacon 80), Staff, Holmes. Subs not used: Harris, Ortega, Nobes.
Stamford: D. Horrigan, W. Donald, A. Peaks, N. Ashby, R. Thompson, M. Green, R. Blowers (G. Pritchard 50), D. Steadman; M. Ndekwe, K. Byrne, K. Ainslie (M. Fisher 78). Not used: R. Yardy, S. Smeathers.
Referee: Culot (Norwich)