Two goals and an assist by substitute Jake Clitheroe in a seven-minute spell made it look much more comfortable for Holbeach United.
Until then, however, they had been hanging onto an early advantage.
The Tigers took control thanks to Stuart Eason’s first goal for the club 15 minutes into his competitive debut.
But a series of missed opportunities along with a hat-trick of saves meant that Swaffham Town ultimately paid the price.
A stoppage-time reply was no consolation for the Pedlars – particularly as goalscorer Alex Vincent had previously wasted enough chances to rewrite the record books.
Although manager Tom Roberts was quick to praise keeper Rick Drury after the game, he had certainly not matched the heroic displays in last season’s FA Cup.
Drury hit the headlines as a spectacular last-gasp goal forced a replay at Worcester City in the second qualifying round in September.
On Saturday, his skills as a shot stopper were not truly tested but at 1-0 up, he denied Vincent three times and those saves proved crucial.
Holbeach were in front as Tommy Treacher released Tyler Wright whose weak shot was rolling wide until Eason slid in.
Yet they allowed Swaffham back into the game and often the Tigers were grateful to see efforts miss the target.
A tactical switch midway through the second half paid off for Holbeach as Clitheroe moved up front.
He set up a golden chance for Eason and within seconds they combined again to make it 2-0.
Stacy Cartwright’s run opened space for Eason who unselfishly squared a pass to Clitheroe for a tap-in.
Two minute later it was 3-0 and effectively all over when Clitheroe set up Wright for a goal on his FA Cup debut.
Clitheroe’s far-post finish opened up a four-goal lead and Swaffham knew that it certainly wasn’t going to be their day when yet another opportunity for Vincent bounced off the far post.
He eventually tucked past Drury after cutting inside from the left flank but that was too little, too late.
Holbeach can’t afford to give away so many clear-cut chances on a regular basis as they won’t get away with it every time.
But some clinical finishing at the other end ensured a safe passage to the next round.
4-4-2: Drury 7; Walton 6, Allen 6, N Jackson 6, Cartwright 6; Thomas 6 (sub Clitheroe h-t, 7), Eyett 6, Warfield 6, Wright 6; Eason 6 (sub Pinner 72 mins), Treacher 6. Subs not used: Coddington, Davis, Portas.
4-2-3-1: Cruickshank; Hutton (sub Loomes 83 mins), Tindall, C Defty, Platten; Keegan, Thompson (sub Allibone 79 mins); Champion (sub Blackford 83 mins), Castellan, Vincent; J Defty. Subs not used: Reed, Watson.
Eason (15 mins, 1-0); Clitheroe (70 mins, 2-0); Wright (72 mins, 3-0); Clitheroe (77 mins, 4-0); Vincent (90 mins, 4-1).
Jake Clitheroe – only came on for the second half due to injury but provided two goals and an assist in a seven-minute spell.
Yaxley (A) – UCL Premier Division, Tuesday.