Jack Lester put Chesterfield in front early on but Sammy Igoe replied before an Alan Connell double sent the Cherries through.
Chesterfield were defending the best home record in the Football League and went ahead in the fourth minute, Wade Small crossing from the left to find the unmarked Lester who made no mistake with a header from six yards.
Bournemouth hit back four minutes later as Liam Feeney's low cross was swept in via a post by Igoe. And the visitors moved in front in the 27th minute, Connell forcing the ball home after an Igoe cross had been headed down by Lee Bradbury.
Connell headed two chances wide early in the second half but made no mistake when he side-footed home in the 76th minute after Brett Pitman's clever dummy.
Chesterfield suffered another blow when Mark Little was sent off for a second booking and only a smart Tommy Lee save denied Pitman a fourth.