The Spireites hammered Pools in a one-sided first-round tie at the Proact Stadium.
The visiting fans turned on their team as goals from Scott Boden, Mark Randall, Craig Clay, Terrell Forbes, Jack Lester and Craig Westcarr booked the League Two club's place in round two, with Antony Sweeney replying for managerless Pool.
Chesterfield went in front in the 16th minute when Danny Whitaker's pass released Boden who lifted the ball over Scott Flinders from 10 yards.
Pools' defence was opened again in the 29th minute when Drew Talbot crossed from the right and Randall side-footed past Flinders from 15 yards.
Veteran striker Steve Howard had a header saved byhome goalkeeper Richard O'Donnell in the 39th minute but three minutes later more awful defending allowed Clay to drive home a free-kick.
Chesterfield scored again in the 54th minute when no-one tracked Forbes' run to the back post to turn in Whitaker's free-kick, and although Sweeney headed in a corner after 78 minutes, Lester drove in the fifth straight from the restart before fellow substitute Westcarr made it six with a 12-yard finish in the last minute.