It was all over by half-time, before Chesterfield rubbed salt into the wounds by hitting their fourth goal and shaking the woodwork twice
Home fans booed the side off the pitch at the end and Manager Brian Carey had to endure calls for his head as he made his way from the dugout to the tunnel after the game.
It went sour after only seven minutes, as goalkeeper Anthony Williams fumbled a left-wing cross from Felix Bastians and the ball ran loose for Jack Lester to stab it into the net.
In contrast Chesterfield keeper Barry Roche made a superb reaction save, turning Mike Carvill's shot around his right post.
Marc Williams fired an early shot which went wide. Chesterfield pushed further ahead with two goals in two minutes.
Adam Rooney finished off another left-wing cross from close range and the in-form Lester headed the third from Jamie Lowry's chip into the box.
A shot from Carvill was no great test for the Chesterfield keeper, though Mark Jones forced him to make a good save.
Defender Neil Taylor also brought a good save from the Chesterfield stopper, who tipped a misplaced centre over the cross bar.
Chris Llewellyn missed Wrexham's next opening with a wild shot well off target.
Wrexham had a bad scare as Chesterfield nearly went four up before the break when Phil Picken's 40 yard thunderbolt rebounded off a post.
The hard working Llewellyn fired another shot off target and saw a header deflected wide.
The fourth goal came on the hour when Peter Leven finished neatly from Lowry's pass.