Strike pairing Jon Walters and Pablo Counago both netted and, although Chesterfield kept going well, substitute Jon Stead netted a third late on.
Chesterfield were first to show with Richard Wright have to race out to clear from Scott Boden, before he dived to turn a Jamie Ward shot round the post.
David Norris shot across goal as Ipswich began to get going and then Tommy Lee comfortably saved a Walters header.
Lee did well to block a Walters shot from Alan Quinn's clever pass and the visiting keeper then parried a fierce drive from substitute Danny Haynes.
Counago volleyed narrowly over and Quinn shot tamely at Lee, but Chesterfield were still a danger and Richard Wright had to save a Jamie Winter header on the line.
Ipswich broke the deadlock on 50 minutes when Phil Picken handled a Quinn cross and Walters lashed home the penalty.
Two minutes later, Richard Wright made a fine save to deny Lloyd Kerry from a Jamie Lowry cross and Ipswich Town went straight up the other end to score, with Counago turning in Quinn's chest down from a Haynes cross.
Richard Wright saved a Lloyd Kerry downward header as Chesterfield tried to get back into the game, but Ipswich were coasting at this point.
They sealed the win on 88 minutes with the goal of the game as Stead volleyed home from Walters' knock-down.