Nuneaton climbed up to third in the Conference Premier table by ending Southport's 100% record.
Louis Moult struck after two minutes with a 12-yard finish but Aaron Chalmers tapped in from close range to level things up six minutes later.
Nuneaton went back in front when Moult netted his second from 18 yards.
Andy Brown saw an effort hit the crossbar for the hosts, who sealed victory after 83 minutes with Adam Walker's 20-yarder.
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