Hayles rounded off some good wing work by Northern Ireland international full-back Tony Capaldi to give the Pilgrims a 36th-minute lead.
However, Wolves goalkeeper Matt Murray was in excellent form and the visitors rallied to level two minutes into the second half after Kevin O'Connor's shot took a deflection off French defender Mathias Doumbe and looped over Argyle goalkeeper Luke McCormick into the net.
Wolves had lost 2-0 to the Pilgrims last April in what represented the high-water mark of Tony Pulis' short reign at Home Park, but there were few similarities to the visitors in terms of personnel or attitude.
The Pilgrims went into the game on the back of a 1-0 defeat at League Two Bristol Rovers but were heartened by the return, after a non-football related injury, of captain Paul Wotton.
It was Wotton who went as close as anyone to breaking the deadlock in a cagey first half, when he forced Wolves goalkeeper Matt Murray to scramble back and claw an inswinging corner over the crossbar. Murray immediately made it a double fingertip save when French midfielder Lilian Nalis headed Capaldi's subsequent corner powerfully goalwards.
Wotton was also prominent at the other end, jumping in bravely to block a shot from former Stoke midfielder Karl Henry as the debutant shaped up menacingly.
The deadlock was broken as the result of a sweet move and some judicious refereeing by Iain Williamson, who allowed Argyle to play on after Nalis was fouled in Wotton range.
David Norris picked up the loose and played Capaldi in on the overlap. His cut-back was nudged towards goal by a stretching Hayles and bounded up towards goal off the committed Murray. The ball was clearly going in as Chadwick applied a final headed touch right on the goal-line.
Argyle maintained their advantage until the interval but only two minutes afterwards. There was a degree of misfortune about it, with Doumbe's outstretched boot deflecting O'Connor's shot up and looping over the stranded McCormick.
Murray, inevitably, had the final word, twisting to stop a clever, reverse-angle shot from Norris after the Pilgrims' player of the year had skinned three Wolves defenders on his way to the edge of the area.