Pulis, who served at the Plymouth helm last season before returning to the Potteries for a second stint in charge, watched as Hayles pounced to cancel out Mamady Sidibe's opener.
Both teams displayed plenty of enthusiasm in the opening exchanges but a distinct lack of confidence in the penalty area saw the half-time score-line confined to a single goal.
Stoke opted for the long ball approach in the hope of capitalising on their obvious height advantage, whereas the visitors looked the team more capable of breaking the deadlock with a fluid passing style.
The industrious Hayles was proving a real handful for the City defence, first teeing up David Norris, who spurned a gilt-edged chance, before having a crack himself.
Tony Capaldi sent in a precision cross for the former Fulham frontman, who saw his bullet header tipped onto the post by the cat-like Steve Simonsen.
Argyle were gathering momentum, and the City rearguard didn't seem to have taken heed from Hayles' first warning shot, allowing him another sight of goal just 10 minutes later.
Some crafty football on the right from Lilian Nalis put Norris scampering through and he unselfishly cut the ball back to the lurking Hayles, causing City to hit the panic button.
Simonsen got down well to save Hayles' first effort, before Clint Hill eventually blocked and cleared the striker's second bite at the cherry.
Plymouth were left rueing their lack of composure in front of the hosts' goal as just five minutes before the half-time whistle, and against the run of play, Stoke stole a first-half lead.
Vincent Pericard, who was last year plying his trade on the south coast with the Pilgrims, pulled the ball back leaving Sidibi the simple task of stroking it home from close range.
City started the second half brightly and should have doubled their advantage when Peter Sweeney was given a sight of Luke McCormick's goal.
The Scotsman smashed a spectacular volley inches over after latching onto a well won header from Sidibi.
But Stoke's backline just could not get to grips with Hayles and in the 78th minute the striker finally got himself onto the scoresheet.
Sidibi failed to clear Paul Connolly's long ball and Hayles nipped in to poke in his third goal of the season and earn the visitors a well-deserved point.