Laurent Mendy broke the deadlock with 30 minutes gone, and club-record signing Luke Duffy secured the win against the Bucks in the final quarter after turning home Tom Peers' cross at the back post.
Saturday's result leaves the Silkmen needing just two more wins to book their place in the first round proper - and with it a potential tie against football league opposition.
It also continues a fine start to the season for a club who currently sit fourth after seven league games upon their promotion to the Northern Premier League.
A number of other NPL sides also booked their place in the next round of the competition - including Warrington Rylands as they thrashed FC United of Manchester 4-0 at Broadhurst Park.
A quickfire double was enough to see Hyde United past Albion Sports, while Simon Grand helped himself to a hat-trick as Lancaster City advanced with a 4-1 win at home to Marske United.
Liam Hughes scored twice for Worksop Town as they eased past Lincoln United, while Morpeth Town and Nantwich Town beat higher-level opposition in Southport and Banbury United.
Whitby Town and Leek Town will also be in the hat for the next round, with five other NPL teams set for replays on Tuesday night.
The draw for the FA Cup third qualifying round will take place at lunchtime on Monday.
Photo credit: Darren Murphy
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