Second-half goals from Jon Walters, Pablo Counago and Jon Stead booked Town a place in the Fourth Round of the FA Cup.
Walters struck from the spot on 49 minutes after Phil Picken handled Alan Quinn's cross.
Richard Wright made a big save from Lloyd Kerry soon after and it proved to be key with Counago making Chesterfield pay seconds later with a left foot finish from six yards after Quinn had headed down Danny Haynes' cross into his path.
Stead completed the scoring three minutes from time with a good finish after Walters had set him up with a header.
Town made two changes to the team that beat Derby last weekend, Counago replacing throat infection victim Kevin Lisbie and David Wright returning to the side after recovering from a hamstring injury, Moritz Volz making way. Connor Wickham, 15, was among the seven substitiutes along with Jordan Rhodes.
Richard Wright cleared from the edge of his box in the first action of note following scrappy play down the Town left that left the 'keeper having to race off his line.
Tommy Miller linked up well with Counago soon after but was judged to have been offside as Tommy Lee made the save in the Chesterfield goal, Wright then saving from the lively Jamie Ward before the first change saw referee Keith Hill replaced by Gary Sutton.
A terrific pass from Counago released Walters down the left, his cross eventually falling to David Norris who shot wide.
Walters headed David Wright's cross at Lee, while at the other end Ward tried an audacious shot from 40 yards that drifted past Wright's goal.
Haynes replaced the injured Miller midway through the first-half, the substitute immediately in the action as he looked to get on the end of a clever backheel from Counago.
Quinn fired wide, Haynes then having Lee scurrying across his goal to clear the ball for a corner after his shot proved too hot for the 'keeper to handle.
Veliche Shumulikoski picked up a fifth yellow card of the season and with it a one match ban after a foul on Kerry as Chesterfield held their own in an even first-half.
Counago had the crowd on their feet with a spin and shot that went just over the angle of post and bar while Ward continued to carry the main threat for the visitors, Ivan Campo making a vital block as the Spireites' frontman shot at goal, Wright making a comfortable save from Aaron Downes' header from the resultant corner.
Haynes' cross was wasted by Quinn at the far post with Kerry booked for a handball in the last action of the opening 45 minutes.
Town got the breakthrough four minutes into the second-half, Quinn's cross hit the outstretched hand of Picken and Walters did the rest from the spot.
Chesterfield should have been level immediately, Kerry denied by Wright from six yards and it proved to be crucial with Counago putting Blues two up seconds later after a cross by Haynes had been headed to the Spaniard by Quinn.
Former Blue Darren Currie replaced Danny Hall, Stead also joining the action on the hour with Quinn making way. The Town substitute bringing a save from Lee low down with virtually his first touch.
Alex Bruce became Town's third change, replacing the injured David Wright with 20 minutes left on the clock. Scott Boden then booked for a foul on Campo.
Kerry headed straight at Wright from seven yards out as the Spireites looked for a way back into the game, Norris then testing Lee at the other end with a low drive.
Chesterfield boss Lee Richardson made his second change with Boden making way for Jordan Bowery for the final 15 minutes.
Stead rounded off the scoring on 87 minutes with a volley after Walters had headed the ball into his path to take his tally to seven for the season, all at Portman Road to secure Blues a place in the hat for Sunday's Fourth Round draw.
Town: R.Wright, D.Wright (Bruce 68), McAuley, Campo, Thatcher, Norris, Shumulikoski, Miller (Haynes 28), Quinn (Stead 60) Walters, Counago. Subs not used: Supple, Balkestein, Rhodes, Wickham. Booked: Shumulikoski
Chesterfield: Lee, Picken, Downes, Hall (Currie 56), Austin, Lowry, Kerry, Winter, Robertson, Boden (Bowery 75), Ward. Subs not used: Algar, Harsley, Goodall, Carson, Askham. Booked: Kerry, Boden
Att: 12,524




















