The home side took the lead through Troy Brown's goal in the 62nd minute, but Henderson struck in the 81st minute to level and he won it in the second minute of added time to life Keith Hill's side up to second.
Neither goalkeeper was seriously tested during an uneventful first period at the Abbey Business Stadium.
The second period started under torrential rain and the deadlock was broken when Craig Braham-Barrett was tripped by Henderson on the Cheltenham left.
Matt Richards' free-kick was cleared as far as Jamie Cureton and he lofted the ball to the far post, where Byron Harrison touched it back for Brown to force over the line.
Rochdale boss Keith Hill responded by making a triple substitution, with Andrew Tutte, Bastien Hery and George Donnelly going on.
The changes almost had an immediate impact, when Joe Rafferty's cross was nodded just wide by Henderson in the 72nd minute
Henderson curled one wide a minute later as the game opened up, with Rochdale pressing for a leveller.
It duly arrived in the 81st minute when Donnelly's cross was nodded past Scott Brown by Henderson and his winner was a perfectly measured chip at the death.