After a goalless first period on Saturday, Bradley Johnson broke the deadlock for the hosts on 56 minutes when heading home Robert Snodgrass’ corner.
But Stoke equalised on 73 minutes via a Walters penalty after substitute John Guidetti had been brought down by Sebastien Bassong in the box.
Walters then turned villain five minutes later when he caught Alex Tettey with a high challenge and received his marching orders before Stoke held on to earn a valuable point away from home and dent Norwich’s push for safety.
Chris Hughton’s side were slow out of the traps as the hangover from the 4-1 mauling they took at Aston Villa last weekend took time to clear and it was in those early stages that Stoke failed to capitalise on their hosts’ anxiety.
Peter Crouch, Marko Arnautovic and Walters all had early opportunities to put Mark Hughes’ men in front and build on their win over Arsenal but once Norwich had settled, the game became much more open.
The first chance fell to Crouch on eight minutes as Glenn Whelan’s through ball split Norwich’s centre-backs but the striker could only shoot tamely at John Ruddy.
Arnautovic was the next man to spurn a decent opportunity to open the scoring as he lashed high over after being found inside the box by Erik Pieters.
Former Ipswich forward Walters then worked Ruddy once more inside the opening 15 minutes after Crouch and Arnautovic combined to create the chance.
At the other end, Wes Hoolahan, who was given a rousing reception by Canaries fans as he kept his place in the side, found Snodgrass with an intricate pass, with the winger bringing a good stop from Asmir Begovic.
Ricky van Wolfswinkel, without a goal since the opening-day draw with Everton, glanced a near-post header wide from a Snodgrass corner as the game moved past the 30 minute-mark with no side able to stamp a telling level of authority on proceedings.
With five minutes to go before the break, the returning Peter Odemwingie was clipped on the edge of the box by Bassong but Arnautovic could only drill a low free-kick well wide of goal.
Hoolahan then tested Begovic from distance after picking up possession as the first half finished goalless.
The first chance of the second half was a replica of Hoolahan’s long-range effort, only this time Begovic could not gather cleanly and was forced to dive back and push the ball behind for a corner.
There was nothing Begovic could do shortly afterwards as Snodgrass whipped a free-kick into the six-yard box and Johnson was on hand to power a header past the Stoke goalkeeper and put the hosts ahead.
Nathan Redmond, who starred for England’s Under-21 side in midweek, came close to adding a second on the hour but his arrowed shot was pushed away by a flying Begovic.
But Stoke, who have only one away league win all season, levelled on 73 minutes as referee Andre Marriner awarded a penalty after Bassong bundled down substitute Guidetti.
Walters stepped up to convert his second spot-kick in as many games – but he could not enjoy his equaliser for too long, as the jeers from the home fans turned to cheers when the Republic of Ireland international was shown a straight red card for catching Tettey high on the leg.
The dismissal prompted Hughton to go on the attack as he introduced both Gary Hooper and Johan Elmander from the bench, with Tettey and the ineffectual van Wolfswinkel replaced.
With 10 minutes remaining, Norwich started to exert the pressure their one-man advantage had given them, with Stoke falling deeper towards their own goal.
But the home side could not muster up a chance to win the game late on as Hughes’ side hung on for a point – leaving the Canaries just four points above the bottom three.