Chesterfield's Jack Lester destroyed Lincoln with a first-half hat-trick.
Lester was left unmarked to score early on and he soon added his second with a shot from inside the box.
He completed his hat-trick with a close-range shot, before Lincoln pulled a goal back when Dany N'Guessan beat two defenders and fired home.
Chesterfield hit a deserved fourth when Adam Rooney's flick was converted by Janos Kovacs, but Lincoln pulled back another with Hamza Bencherif's header.
Lincoln City: Marriott, Green, Moses, Bencherif, Croft, N'Guessan, Frecklington, Kerr, Hand (Wright 46), Torpey (Forrester 46), Dodds.
Subs Not Used: Duffy, Amoo, Hone.
Booked: Kerr, N'Guessan.
Goals: N'Guessan 44, Bencherif 67.
Chesterfield: Roche, Picken (O'Hare 86), Robertson, Kovacs, Downes, Rooney, Niven, Leven, Bastians (Gray 72), Lester, Ward (Fletcher 72).
Subs Not Used: Smith, Winter.
Booked: Downes, Ward, Picken, Leven.
Goals: Lester 8, 18, 42, Kovacs 65.
Ref: Ray Lee (Essex).