Argyle trailed 1-0 to a well-taken 67th-minute strike by Tom Barkhuizen, who converted from close range after a superb pass from Harry Pell.
But the Pilgrims were thrown a late lifeline when substitute striker Warren Feeney was tumbled in the area by Nicky Featherstone and Chadwick, on loan from Stockport, coolly crashed in his second goal in two home games in the 81st minute.
Three minutes later Hereford were reduced to 10 men when central defender Michael Townsend received his second yellow card following a foul on Argyle’s pacy winger Ashley Hemmings.
Feeney forced a brilliant save from Bulls keeper Adam Bartlett as Argyle pressed for a winner and should have done better with a volley seconds later.
In stoppage time, Argyle central defender Darren Purse – who had earlier headed against the crossbar – was red-carded for a foul on Nathan Elder.