Bury Town made hard work of beating their Ridgeons League opponents despite the hosts playing for nearly an hour with ten men, with the tie only made safe with four minutes to go.
Walsham had the better of the early play and Jack Brame forced a good save from Marcus Garnham.
Little had been seen of the Bury attack, but they took the lead on 23 minutes. Home keeper Duncan McNally came well out of his goal as Kieran Leabon squared the ball for Danny Cunningham to fire into an empty net.
Leabon then missed a good chance to double the score but shot wide from close range. Bury were now well on top and Walsham were reduced to ten men after 31 minutes when Paul Musgrove was sent off for a second yellow card.
Four minutes later Craig Nurse scored Buryâ€™s second with a fine shot on the turn from the edge of the box after a period of sustained pressure.
Half Time: Walsham Le Willows 0 Bury Town 2
Bury came close to a third goal at the start of the second half when McNally failed to hold a Lee Reed shot but the ball went wide.
Walsham reduced the arrears on 54 minutes from the spot after Lee Reed was adjudged to have fouled just inside the box. Brame duly scored the resultant penalty.
Nurse then had a header cleared of the line, but despite having more of the possession, Buryâ€™s final ball often lacked accuracy and few chances were created.
With four minutes to go, Bury made the game safe when Sam Nunn rose to head home from a Lee Reed corner, to put them into the next round.
Full Time: Walsham Le Willows 1 Bury Town 3