The Hornets dominated the second half as they looked to respond to Joe Haigh’s 36th minute goal.
Reece Myles-Meekums hit the woodwork and Daggers keeper Sam Howes made several top saves to deny the hosts.
But the former Horsham stopper was given his marching orders deep into stoppage time after kicking out at Jack Strange.
The referee pointed to the spot and Hammond duly slotted home the Hornets’ equaliser.
The draw sees Horsham drop to ninth in the National League South.
Horsham visit 14th-placed Slough Town this Saturday and relegation-threatened Enfield Town – who the Hornets were due to play last weekend – on Tuesday.
See McCartney Martin’s pictures from Horsham v Dagenham & Redbridge on this page and the ones linked – and get Dominic Di Paola’s view on the action in the West Sussex County Times, out on Thursday.
21. Late penalty snatches point for Horsham FC against Dagenham – the match in pictures
James Hammond netted a penalty deep into second half stoppage time to secure a point for Horsham FC against Dagenham & Redbridge on a night of high drama at the Fusion Aviation Community Stadium. Photo: McCartney Martin