The 22-year-old, who has three caps and is being tipped as England's future regular No.1, made superb saves from Alex Oxlade-Chamberlain and Olivier Giroud, twice, including stopping a header by the Frenchman that looked destined for the bottom corner.
Arsenal manager Arsene Wenger was philosophical about the injuries that have forced him to reshuffle his team in recent weeks and said he hoped striker Alexis Sanchez and playmaker Mesut Ozil would be back to face Chelsea in the league next week.
Losing Ozil to a slight foot injury before the match was a blow, he told Sky Sports. "There is not a team in the world that would not miss Mesut," he said, adding that he was pleased with the point from a tough physical match.
"Even with Mesut it would have been a very difficult game" he said, "but spirit-wise we were fantastic and we came away with a positive result compared to other results we have had here."
While Butland did well at one end, Arsenal keeper Petr Cech performed enough heroics at the other to earn him the Man of the Match award.
He twice denied Austrian striker Marko Arnautovic after the break and also thwarted a follow-up shot from Bojan Krkic at the end of a swift Stoke counter-attack.
Stoke went close to a winner in the dying minutes but Aaron Ramsey and Cech combined to clear two goal-bound attempts and, like Wenger, Stoke manager Mark Hughes seemed reasonably satisfied with a point from the draw.
"I thought we played well and I enjoyed it. I thought we were very much in the game and in the first half I thought we were the better team.
"In the second half I thought Arsenal came into it a little bit more and played it around our box more, but they didn't really create anything of note apart from the number of saves Jack made."
The result left Stoke in a healthy seventh place on 33 points, six points off the top four.
(Reporting by Mike Collett; editing by Martyn Herman and Ken Ferris)
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