Chesterfield's win keeps them in the chase for the play-offs and leaves AFC Wimbledon bottom of League Two.
Armand Gnanduillet stroked Danny Whitaker's cross into the top corner to score his first goal in English football and break the deadlock.
Neil Sullivan saved Drew Talbot's 20-yard drive, but the Dons would eventually fall to a 16th league loss.
Jack Lester sealed it for the hosts, firing a low shot past Sullivan after being set up by Gnanaduillet.
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Chesterfield manager Paul Cook told BBC Radio Sheffield:
"It was a game that if we didn't win today it would make it a challenge to get in the play-offs.
"Every point is vital and today I told the lads at half-time that this is our season.
"We must remain strong and patient and to the man I felt we did that."