The north Londoners struggled to test Asmir Begovic in a physical contest at the Britannia Stadium, with Laurent Koscielny's hand ball gifting victory to Mark Hughes' side
With the game heading towards a goalless draw, Laurent Koscielny was adjudged to have handled Walters' flick inside the box, and the Republic of Ireland international stepped up to dispatch the penalty and dent the Gunners' title hopes.
The result continues the Potters' fine form against Arsenal, with Arsene Wenger's men having won just once of their last 10 trips to the Britannia in all competitions, and extends the Gunners' winless run on the road to three matches.
Wenger took the decision to leave Mesut Ozil on the bench, with the German having also missed the 4-1 win over Sunderland, while Koscielny was fit enough to start despite suffering an injury against the Black Cats.
The two clubs have endured a fractious relationship in recent years and that was in evidence once again as a series of fouls frequently halted play, while clear-cut chances remained conspicuous by their absence.
But Stoke began to assert its dominance after the half-hour mark. Steven Nzonzi, selected in place of the injured Peter Odemwingie, saw his cross deflected into the path of Peter Crouch, whose shot rippled the side netting.
Glenn Whelan was then perhaps fortunate to avoid a booking from referee Mike Jones when he appeared to catch Olivier Giroud's knee in a challenge eight minutes from the break, before Jack Wilshere almost got on the end of Giroud's teasing through ball.
Fortunately for the hosts, the Frenchman's pass was a touch too strong, with just enough time remaining in the half for Whelan to test Szczesny from distance.
Crouch fired an acrobatic effort wide of the Arsenal goal within six minutes of the restart and he should have opened the scoring shortly after when he failed to divert Charlie Adam's cross past Szczesny.
In a rare Arsenal burst, Wilshere looked set to break through the hosts' defense but the Stoke back line stood strong to deny the England international as they continued to stifle Arsenal's creativity.
After Crouch went close again with a header from Adam's cross, Geoff Cameron fired wide from inside the area - with Wenger opting to introduce Ozil from the bench in an attempt to offer a threat.
However, Stoke seized on its best opportunity of the match after 76 minutes when Koscielny handled inside the penalty area.
Walters, despite having shown inconsistency from the spot in the past, calmly stroked the ball home to hand the hosts the lead and, while Ozil fired an effort wide eight minutes from time, the Gunners were unable to mount a response as Arsenal's Stoke hoodoo continued.