Bradley Johnson had headed Norwich in front early in the second half before captain Sebastien Bassong was adjudged to have fouled substitute John Guidetti inside the penalty box.
Former Ipswich man Walters converted the resulting penalty but his adulation lasted less than five minutes as he was dismissed for a dangerous challenge on Canaries' midfielder Alex Tettey - although Norwich could not find a winner and had to settle for a 1-1 draw.
Hughton's side were slow out of the traps as the hangover from the 4-1 mauling they took at Villa Park 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 real chance of the game 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 Ruddy's crossbar after being found inside the box by Erik Peters.
With unease spreading amongst the Norwich supporters at such an early stage, former Ipswich forward Walters worked Ruddy once more inside the opening 15 minutes after Crouch and Arnautovic combined to create the chance.
Nathan Redmond, who starred for England's Under-21 side in midweek, did well to skip past a couple of Stoke challenges on the edge of the box but his ball to Snodgrass was a little in front of the Scotland international and his cross squirmed harmlessly out for a goal-kick.
Wes Hoolahan was given a rousing reaction by the Canaries' fans as he kept his place in the side and the diminutive playmaker found Snodgrass with an intricate pass, with the winger this time able to bring 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.
Almost any attack of note for the hosts stemmed from Hoolahan and the Irishman tested Begovic from distance after picking up possession and driving into Stoke territory.
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.
Redmond came close to adding a second on the hour but his arrowed shot was pushed away by a flying Begovic.
Stoke, who have only one away league win all season, levelled with just under 20 minutes remaining 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, much to the chagrin of the home fans.
But Walters could not enjoy his equaliser for too long as the jeers from the home fans turned to cheers as 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 and 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.