Liam Ridehalgh struck a spectacular first career goal to move Chesterfield off the bottom of League One.
Bournemouth had plenty of first-half possession but the best chance fell to Chesterfield when Jack Lester fired a shot against keeper Darryl Flahavan.
Flahavan denied Lester with an even better save after the restart but he was helpless when Ridehalgh drove an unstoppable shot into the top corner.
Spireites keeper Tommy Lee denied Wesley Thomas a late equaliser.
The Spireites' win enabled them to swap places with Rochdale who were left in bottom place prior to their fixture against Bury.
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Chesterfield manager John Sheridan tells BBC Radio Sheffield:
"It's a great result for us, we know what we have to do in the position we are in, we've got to win football matches.
"The most important thing is we've come out with three points, but I thought it was a very, very good performance for us against a very good team in my eyes.
"They've got a great record away from home and they may have thought they would have come here and turned us over, but full credit to my players."
Bournemouth boss Lee Bradbury told BBC Radio Solent:
"For long periods of the game we had possession of the ball, passed the ball well, but lacked a bit in the final third today. It took a great goal to open us up though, and we gave it a good go in the last 25 minutes.
"We didn't have a many chances as we usually do, and credit to them for that. They got in our faces and made it difficult for us to play. Even though they did, I felt we were calm on the ball... we did cause them a few problems, but not too many in front of goal.
"Chesterfield didn't show they were bottom of the table tonight, they worked very hard for each other tonight, and if they play like that most weeks, then they'll be alright."