An 18th minute goal from former Lynn favourite Michael Gash had Sports dreaming of a first ever appearance in the first round proper of the greatest knockout competition of them all.
But Lynn hit back to equalise on the stroke of half-time before a goal on the hour mark ultimately sent the National League side through.
Sports pressed hard for a leveller in front of just over 1,000 fans at the Walks, but their heroic effort fell just short.
The first period of the game was a fairly tight affair, with the hosts having the balance of midfield possession without troubling Lewis Moat.
But on 18 minutes Sports found the breakthrough and it was written in the stars for it to be Gash with the goal. A superb Luke Warner-Eley ball fell to Gash who took the ball down well and fired home.
This served to wake up Lynn and they started to fashion some good chances, but were unable to equalise until added time in the first half when a corner was well headed home by the big number nine Gold Omotayo.
The first real action of the second period was on 48 minutes and a superb ball from Dan Lawlor found Jordan Nicholson who drove in, fed Dion Sembie-Ferris, but his first time shot was well saved by ex-Posh ‘keeper Paul Jones.
Six minutes later the Linnets had an excellent chance they were unable to convert, but this led to a serious looking injury to Rowley who had to be stretchered off and replaced, which led to a seven-minute stoppage.
On 61 minutes Kings Lynn took the lead with a deflection falling to McGavin who fired home.
Nicholson had a great chance on 77 minutes to equalise for Sports, but he was to be foiled by a superb block on the line by Fernandez and the resulting corner was headed goalward, but cleared by Jones.
Sports began to press more and more as the clock wound down and due to the serious injury earlier there was 10 minutes of injury time.
Sports had several good chances to equalise, with Nicholson shooting narrowly wide and Richard Jones unable to convert from just outside the six yard box and the last chance was a direct free kick to Sports from just outside the box, but Lynn were able to keep Sports out.
So on the final whistle Sports bowed out of the Emirates FA Cup for this season, but it was a valiant effort and at no point did the sides look to be two divisions apart.
It was a magnificent effort from the travelling Turbines army of over 200 fans as well as they sung and encouraged the Sports players through the whole match. This was fully appreciated by the Sports management and playing staff who came over to applaud them at the final whistle.
Sports have a huge Southern League Premier Division game at Coalville on Tuesday (October 19). Leaders Sports are four points clear of their second-placed hosts.
King’s Lynn Town: P. Jones, Fernandez, McFadden, Clunan, Coleman, Omotayo, McGavin (Gyasi 82), A. Jones, Sundire (Linton 46), Barrows, Rowley (Barrett 55).
Peterborough Sports: Moat, Bazeley, Warner-Eley (Herd 65), Fryatt, R Jones, Lawlor, Sembie-Ferris, McCammon (M. Jones 90), Gash, Jarvis (Stevenson 53), Nicholson. Subs not used: Elsom, Miles, McGowan, Moreman.