Midfielder Jones found the corner from 25 yards in the second half after receiving the ball from Matt Palmer.
Aaron Amadi-Holloway shot just wide earlier on, with Spireites keeper Tommy Lee doing well to foil Curtis Main.
Lee also tipped over Tommy Thiele's volley following the goal, while Chesterfield failed to muster a clear-cut chance despite late possession.
Oldham remain in the bottom four despite the three points, but behind Fleetwood on goal difference only, while the visitors are just two points above them in 18th place.
Oldham boss John Sheridan told BBC Radio Manchester:
Media playback is not supported on this device
"I thought we thoroughly deserved the three points.
"First half, I thought we were the better team, had one or two half chances. Their keeper has been involved a lot more than ours has.
"We kept going and pushing on, leading up to the goal. Obviously (we were) panicking in the last probably 10 minutes, they were throwing balls in the box and we're a bit edgy clearing things. It's a massive win for us.
"It's about the team, not the individuals, me or anyone, it's about us as a group. As a team, we were probably a seven out of 10, and that's what got us the result."
Mike Jones scored a crucial winner for Oldham against Chesterfield to improve their chances of avoiding relegation.