Town, who reverted back to the starting line-up that thrashed Salford last weekend, were under early pressure with Jon Kennedy saving well from Dave Walker.
But Halifax went in front after 10 minutes when Paul Gedman flicked the ball on for Peter Mo
ore who fired home from 15 yards.
Cavell Coo volleyed across goal and wide form a Jonathan Smith cross soon after but Nantwich levelled in the 16th minute when Alan Naggington fored home from a Parker pass.
Naggington might have had a second but was denied by Kennedy's legs and a Dave Tickle shot flashed across the face of the Town goal and wide.
Substitute Nigel Jemson - on for Gedman - headed down and into the keeper's arms on the stroke of half time.
Kennedy saved well from Tickle early in the second half while Payne headed over from a Smith free kick.
Nantwich hit the front for the first time in the 57th minute when Glyn Blackhurst headed home a Tickle corner.
Payne headed over from a Smith free kick soon after but Nantwich added to their lead in the 66th minute when Walker fired home from the penalty spot after Lincoln Adams had fouled Michael Lennon.
And Walker added the fourth with five minutes remaining when he got on the end of Liam Shotton's flick.
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