Chesterfield are still awaiting their first league victory under new boss Paul Cook.
Rovers took a fifth-minute lead when Eaves made space for himself on the left side of the penalty area and his low cross was turned in at the far post by Chesterfield's Sam Togwell for an own goal.
Mark Randall claimed the visitors' 20th-minute equaliser as his innocuous free-kick from the left touchline was carried over his own line by Rovers goalkeeper Neil Etheridge under no pressure as he stretched to gather.
Joe Anyinsah slid in to fire Rovers back in front from another Eaves cross after 59 minutes, only for Spireites substitute Brennan Dickenson to find the top corner with a bullet shot from the corner of the box to make it 2-2 soon after.
Both sides hit the woodwork in the second half, but it was left for Eaves to have the crucial say when his 20-yard shot was deflected home in the 80th minute, piling further misery on Cook in what was his third league match in charge of Chesterfield.
