Stamford chairman Tim Clancy, who had predicted an FA Cup win for the Daniels, gave the Linnets generous praise for their performance.
"King's Lynn played an excellent game and I wish them all the best in the next round. They looked to be in top form." he said.
Last week Clancy had said he did not think Lynn were good enough to beat his United Counties League side.
"We gave him a good answer on the field," said Lynn player manager Frank Wignall, after the match.
"I thought that everyone worked well and hard, now let's hope we can maintain this enthusiasm in the league. These boys have set their own standard in enthusiasm and football."
Stamford manager Norman Rigby, who had a lot of FA Cup gory with Peterborough a few years ago, was also full of praise for the Linnets.
"I think it was a fair result. Lynn were the better side on the day and we did not play as well as we have done recently but this may have been because of the opposition."
Watched by a 1,200 plus crowd, the biggest at The Walks for nearly two years. Saturday's Fourth Qualifying Round tie did not live up to expectations in the first half.
Most of the play saw Lynn pushing forward from midfield - where Tony Woolmer was more involved than in any other game this season. The Linnets forced ten corners in the half and just before the interval one from Malcolm Lindsay was missed by keeper Dick Bonney, but Mick Wright an John Durant got in each other's way as they went for the loose ball.
Best chance of the half had fallen a few minutes previously - the 30th - when Lindsay headed over from close range.
Stamford had relied on the speed of winger Gerry Fell and the height of striker Dick Smith, but they had few chances. Garry Steel was rarely worried as he made his return after missing none matches.
Stamford had shown themselves to be a better side than many people had expected in this first half, but their defence wilted under strong pressure straight after the interval.
Bonney was at a loss with a shot from Wignall which ran along the face of the bar, then was clearly beaten by another shot from the Lynn manager which rebounded off the bar.
The breakthrough came in the 58th minute from amateur Durant. Last season Durant impressed a number of fans with his few first team games, but this season he had not been given a first team outing until Saturday.
It was a golden return - just as Ron Caley had scored in his debut in a previous tie against Clacton.
Durant took a headed pass from Rudd on the left wing and sped past Phil Harris before lofting the ball over Dick Bonney into the corner of the net. Norman Rigby said later: "I think it was lucky goal. It seemed to me the lad meant it as a centre."
A minute later John Richardson crashed a 20 yard shot against the post as Stamford fell to pieces. But the Daniels could not get the ball away and going past Ron Cooper, Keith Rudd calmly side-footed his shot past Bonney after a feint had sent the goalkeeper the wrong way.
It now looked easy for the Linnets. They were two up and their defence looked on top form.
But a misunderstanding between Trevor Painter and Garry Steel let in Fell, who hooked in an angled shot to put Stamford back in the game in the 64th minute.
This was the only slip-up in the Lynn defence. Painter and Wright were commanding in the middle, Richardson and Smith strong on the flanks. Smith had the job of marking Fell and did extremely well - especially in the second half when he made a number of important tackles and interceptions to turn defence into attack with bursting runs down the wing.
One such move in the 80th minute opened the way for Rudd, but his shot went inches the wrong side of the post.
The clinching goal came in the 86th minute and it was a well-worked affair.
Richardson and Brooks started it in midfield, Wignall took over with a snap pass to Rudd who turned it into the path of Durant who quickly shot hard and low past Bonney.
Later Wignall said of Durant: "He did very well for us with a lot of running and he scored two good goals."
Attendance of 1,262 on Saturday was the largest at The Walks since 2,474 fans watched the FA Cup 1st Round tie against Hereford in November 1971
|Lynn: Steel, Richardson, Smith, Brooks, Painter, Wright, Durant, Rudd, Lindsay, Wignall, Woolmer. (Sub Elliott).
Stamford: Bonney, Best, Marchant, Kwiatkowski, Cooper, Harris, Fell, Jaggard, Smith, Adams, Barnes. (Sub Russell for Jaggard 63 mins).
Referee: D Hutchinson (Cambs). Attendance: 1,262.