The Spireites headed into Friday night’s game at the B2Net Stadium knowing victory would lift them from the foot of the table for the first time since November 5.
But they were under no illusions about the challenge facing them against a Cherries side that had not lost on the road in five months.
Bournemouth had enjoyed good spells of possession in the first half but the only chance fell to Chesterfield in the 41st minute when a mistake let Jack Lester in, only for his shot to ricochet off the legs of Darryl Flahavan.
The keeper made an even better save at the start of the second period, diving to turn behind a low drive from Lester. But he could do nothing when Ridehalgh drove an unstoppable shot from the left edge of the area into the top-right corner in the 55th minute.
Bournemouth responded by forcing Tommy Lee into his first save of the game as he denied Wesley Thomas in the 69th minute. That proved all they could muster, though, as the Spireites claimed a second win in seven days.