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Chesterfield soon equalised when Gardner fired in following Roberts's quick free kick.
Roberts then got one himself when he lobbed Northampton keeper Matt Duke seven minutes after the break to give Chesterfield the lead.
The goal signalled a period of Chesterfield dominance, with Northampton's defence struggling with the muddy conditions.
The Spireites eventually secured the points three minutes from time when Gnanduillet drove home following good work from Ian Evatt.