Kellermann found the corner of the net from the edge of the box just before half-time for his second goal of the season and it proved to be the winner.
Yeovil had some chances and were competitive throughout but they could not find an equaliser.
The victory was Paul Cook’s first since returning to the Blues and it keeps them second in the table.
Here are Liam Norcliffe’s player ratings from the match...
Scott Loach 7
Clean sheet. Made a fantastic point-blank save to tip over Wilkinson’s close-range header in the first-half with the game goalless. He was more assured in everything that he did.
Jeff King 6
Back in the side after his suspension. A bit rusty in the first 45 but livened up after the break.
Laurence Maguire 7
A solid outing. Came close to scoring in the first-half when his glancing header from Whittle’s deep cross was saved by a great fingertip stop from Smith.
Jamie Grimes 7
Dominant in the air and apart from a few stray passes he did well. Captained the side.
Alex Whittle 7
A steady outing up and down the left. Put in a good shift and not much got past him.
Jim Kellermann 8
His stunning half-volley from 20 yards gave the Spireites the lead just before half-time. He did a fine job sitting deeper in midfield in the second 45. An extra mark for the brilliant goal.
Tom Whelan 7
A performance which had a bit of everything. Battled really well. A good, all-round midfielder’s performance.
Liam Mandeville 6
A quiet game by his standards. The energy he showed against Wrexham was not quite there. In fairness, Yeovil did not give him much space to work in.
Calvin Miller 7
Sloppy first-half but really improved after the break when he switched to the right flank and he gave Town a good outlet with his dribbling.
Akwasi Asante 6
Had Chesterfield’s first sight of goal when he fired wide from inside the area in the opening 20 minutes. Switched to the left after the break and was fairly quiet but worked hard.
Joe Quigley 6
He put himself about against his former club and certainly put in a lot of work off the ball. His best chance at the near post in the second-half was well blocked. Came off to applause midway through the second-half.
Tom Denton 6
A good 25-minute run-out for the big man. His most important contributions came in Town’s box with some defensive headers.
Saidou Khan N/A
Replaced Mandecille late on.