In a game which saw three penalties, Marc Richards put the Spireites into the lead on 18 minutes before Danny Hattersley likewise converted from the spot seven minutes later.
Chris Almond scored what proved to be the winning goal midway through the second half before Aaron Chapman saved a late penalty at the The Merseyrail Community Stadium.
Cook fielded a strong starting line up as Chesterfield stepped up their preparations ahead of the season’s opener at Bury in two weeks’ time.
Full match report to follow.
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Chesterfield: Lee (Chapman 75); Talbot, Hird (Brown 70), Cooper, Humphreys (Smith 62); Morsy (Togwell 50), Ryan (Bencherif 68), Darikwa (Doyle 50), O’Shea, Roberts (Devitt 70); Richards (Gnanduillet 50). All subs used.
Southport: Hurst; Challoner (Joyce 75), Fitzpatrick (Willis 60), Chalmers, Flynn (Akrigg 60), George, Rutherford (Osawe 60), Milligan, Hattersley, Brown, Almond. Subs not used: Smith, Kearney, Sumner, Fazel, Livesey, Campbell, Ojapah.
Referee: Mr Matty Parry