The Republic of Ireland international converted his second spot-kick in as many weeks after Bradley Johnson had put the hosts ahead in the second half, before being shown a straight red card five minutes later for a high challenge on Alex Tettey.
Midfielder Johnson had given the hosts the lead after 56 minutes, heading home Robert Snodgrass' free-kick from close range, and for a time it looked as though Stoke were set for a sixth league defeat out of seven on their travels.
The former Ipswich Town man's afternoon then soon turned sour though, when he was given his marching orders by referee Andre Marriner for a dangerous challenge on Tettey which left the midfielder writhing in agony on the turf.
The result did little to help either side's fight to avoid relegation, although having fallen behind and then holding out for the final 12 minutes a man light, Mark Hughes' side will be happier with the draw.
The visitors were without Charlie Adam, the influential midfielder beginning a three-match for a stamp on Arsenal's Olivier Giroud, but made light of his absence early on, and should have been in front after creating three presentable chances in the opening 15 minutes.
After a sluggish start the hosts began to assert themselves, with Asmir Begovic tipping Snodgrass' angled drive away in the 28th minute before the Scotland international sent in a corner that was headed across the face of goal by Ricky Van Wolfswinkel five minutes later.
Begovic almost made a costly error eight minutes after the break, scrambling back to claw the ball away from the goalline after parrying Wes Hoolahan's initial effort up into the air.
Three minutes later Norwich were in front, Johnson rising highest to meet Snodgrass' right-wing free-kick and thump home a header from six yards.
Nathan Redmond almost doubled the home side's advantage on the hour-mark, sending in a rasping drive from 25 yards which Begovic saved with a strong hand.
Walters then took centre stage, cooly converting the spot-kick after Bassong's foul on Guidetti, before tarnishing his efforts with a clumsy knee-high challenge on Tettey that earned him his dismissal.
