Never say die Wolves were not to be denied however and were rewarded when Cort stabbed home his 14th goal of the season.
But the shine is likely to be taken off their late heroics as they face the threat of a probe by the Football Association.
Stoke centre half Michael Dubbery was struck by at least one coin thrown from the Jack Harris stand while he was having treatment in the second-half.
Referee Chris Foy seems certain to include the incident in his match report.
Wolves should not have needed Cort's late show as they had dominated enough of the game to have won it but were frustrated by goalkeeper Steve Simonsen who starred for Stoke in the second-half.
Wolves dictated the first half in terms of possession, but they could not make that pay and were undone by Noel-Williams.
City threatened as early as the eighth minute when the impressive Dave Brammer hit the bar with a curling free-kick.
Wolves then enjoyed their best spell of the half with Simonsen denying Ki-Hyeon Seol and Rob Edwards, before Kenny Miller and Cort fired wide from good positions.
Having successfully weathered that storm, Stoke stunned Wolves when Noel-Williams broke the deadlock.
The goal was a personal disaster for Miller. The Scottish international was picked out by a pass from Edwards only to lose possession to Clint Hill.
Central defender Hill surged forward to the edge of the Wolves area before sliding a pass into the path of Noel-Williams who beat goalkeeper Michael Oakes with an angled drive.
Hill and Noel-Williams combined again six minutes into the second-half but this time the former Watford marksman failed to trouble Oakes when he pushed his shot wide.
Wolves then went on a frantic search for an equaliser only tobe frustrated by Simonsen.
He tipped a stinging 58th-minute drive from Mark Kennedy around the post and then pulled off another top class save from Seyi Olofinjana three minutes later.
Simonsen's heroics looked good enough to earn Stoke a vital win before Wolves launched their late push.
Lee Naylor lifted a free-kick into the area and it was headed on by Seol into the path of Cort, who calmly side-footed past Simonsen.