Spireites lost out to a 50th minute goal from the reigning League One Player of the Month Adam Armstrong.
He turned on a ball from the impressive Jacob Murphy to pirouette just inside the box and fire home his 6th goal of the season beyond Tommy Lee.
Chesterfield, forced to make two substitutions due to injury, saw one of the replacements, Mani Dieseruvwe, sent off near the end when he attempted to punch the ball in having been booked for a foul earlier on.
For the vast majority of the game, the visitors were second best. With Murphy and Liverpool loanee Ryan Kent, making his first ever league start, almost impossible to keep at bay, the Sky Blues forced Tommy Lee to make plenty of saves and they forced 13 corners as well as they dominated possession. Sylvan Ebanks-Blake did have the ball in the net but he was clearly offside and home keeper Lee Burge had to tip over from debutant Chris Herd and a tip round from Dieseruvwe.
Coventry had a hatful of chances to double their lead but they were continually thwarted by a game defence who, by the end of the game, were virtually all acting as supplementary attackers.
Coventry: Burge, Stokes, Vincelot, Johnson, Fleck, Armstrong, O’Brien, Ricketts, Martin, Murphy, Kent. Subs: Charles-Cook, Thomas, Lameiras, Morris, Phillips, Tudgay, Antoine-Fortune.
Chesterfield: Lee, Herd, Hird, Evatt, Jones, Morsy, O’Neil, Gardner, O’Shea, Novak, Ebanks-Blake. Subs: Cairns, Raglan, Humphreys, Banks, Ariyibi, Dieseruvwe, Gnanduillet.
Ref: Darren Bond (Lancashire)