James Brown scored twice as Hartlepool eased into the second round of the Johnstone's Paint Trophy at Saltergate.
David Foley put Pools ahead after latching on to Richard Barker's pass.
Barry Roche denied Foley a second and Josh Law almost drew Chesterfield level before Brown scored a superb solo goal, beating three men and chipping home.
Brown then converted Michael McKay's cross to make it 3-0 but veteran striker Wayne Allison scored from 10 yards to make it 3-1 late on.
Chesterfield: Roche, Picken (Law 21), Robertson, Kovacs, Jackson (Algar 55), Gray, Lowry, Niven, Winter (O'Hare 58), Rooney, Allison.
Subs Not Used: Jordan, Williams.
Booked: Niven, Winter, Lowry.
Goals: Allison 72.
Hartlepool: Budtz, Nelson, Brown (McCunnie 61), Antwi , Clark, Liddle, Humphreys, Gibb, Robson (Foley 17), Barker (Mackay 54), Porter.
Subs Not Used: Lee-Barrett, Turnbull.
Booked: Liddle, Antwi , Gibb.
Goals: Foley 34, Brown 51, 59.
Ref: Steve Bratt (W Midlands).