Boston United joint boss Lee Canoville praised his side after they battled to a 1-0 FA Trophy win over Workington.
Marc Newsham scrambled the 58th-minute winner from Ben Milnes' free-kick to earn a first-round tie at home to Hyde.
Canoville told BBC Lincolnshire: "It was a very scrappy game, neither side wanted to lose but we stepped it up in the second half and we're through.
"A few weeks ago we could have drawn or even lost that game so we're moving in the right direction."
In a game of few chances, Danny Sleath also went close for the Pilgrims, while keeper Paul Bastock pulled off a triple save just before the break to deny the visitors, for whom Davd McNiven struck the woodwork in the second half.
Canoville added: "Sometimes you just have to dig in. We knew they would come here and make it difficult, they had their gameplan and in the end we had to adapt but overall I'm happy we're in the next round."
The first round tie against Hyde will be played on Saturday, 10 December.