Coventry City remain two points behind fourth placed Notts County in the League Two table.
Notts County could have gone within a point of third placed Wycombe Wanderers, had they won at Chesterfiield, this afternoon.
However, a crowd of 6,005 saw Nelson put Chesterfield ahead in the 16th minute with Hines adding a second in the 39th minute.
Jones did pull a goal back but Chesterfield had a penalty which Dennis put away in the eighth minute of second half stoppage time to give the Spireites a 3-1 win to put them now three points behind third from bottom Grimsby Town and keep Notts County in touch with the rest of the teams currently in the play-off positiions.