STRIKER Danny Bloomfield booked the Linnets a place in the last eight by converting a 59th minute penalty at the Newflame Stadium on Tuesday night.
Bloomfield made no mistake from the spot after the impressive Ludovic Quistin had been impeded in the box.
Linnets boss Tommy Taylor was pleased with his side's display and a clean sheet, saying: "Our midfield was a bit more solid and that made a big difference on the night."
The return of defender Adam Jones allowed Taylor to put Mark Camm in the centre of midfield alongside Sam McMahon.
John Higgs replaced Steve Wilson between the posts, while Robbie Harris made his first appearance for the first team for three months and did enough to impress Taylor.
"I thought Robbie did very well for us, but I took him off because he got a bit of a knock," said Taylor.
"Spalding have been back on the phone wanting to take Robbie on loan again, but I've told them no."
Lynn always had the upper hand with Stamford seemingly having one eye on their big fourth round FA Trophy clash at the weekend.
Quistin could have had another penalty earlier in the proceedings, while Bloomfield struck the woodwork:
Substitute Jack Defty missed a great chance to wrap things up near the death when he sidefooted an Angel pass wide of the target.
Lynn: Higgs, Jones, Chick, Clark, Hammond, McMahon, Camm, Hay (Defty), Harris (Holmes), Bloomfield, Quistin (Angel), Subs not used: Ward and Wilson. R
MoM: Ludovic Quistin.