The Gunners have won just once in five matches at the Britannia and struggled to break down a determined Stoke defence, who had chances to claim their own first win of the league season.
Stoke started the brighter side and, buoyed by a vociferous home crowd, had a 'goal' ruled out early on for offside.
Jonathan Walters found the net from a Peter Crouch knockdown but referee Lee Mason halted the celebrations.
Arsenal had numerous chances to break the deadlock before half time as they adjusted to life without van Persie, in their first away game since the Dutch striker moved to Manchester United.
A Lukas Podolski shot was blocked by Andy Wilkinson with replays suggesting an arm may have been used by the Stoke defender.
As was the case against Sunderland on the opening day of the season, new Arsenal midfielder Santi Cazorla, a summer signing from Malaga, enjoyed plenty of possession in midfield.
It was Cazorla who fired wide after his initial free-kick had hit the Stoke wall as Arsenal searched for the breakthrough.
Cazorla forced Asmir Begovic into a save before Podolski blazed over the crossbar.
It was not all one-way traffic though and Stoke offered a renewed attacking threat of their own.
A tame shot from the right from Wilkinson was comfortably gathered by Arsenal keeper Vito Mannone, in the side because Wojciech Szczesny failed a fitness test on a rib injury.
Mannone then saved well from a fiercely struck shot by Michael Kightly, Stoke's summer signing from Wolves.
The visitors could have had the lead before the break when Mason played advantage after Mikel Arteta had been felled in midfield, and Cazorla's bending effort forced a save at full stretch from Begovic.
The second half started slowly before Jermaine Pennant, the former Arsenal midfielder, had claims for a penalty waved away by Mason after a coming together with Kieran Gibbs.
Stoke manager Tony Pulis brought on forward Cameron Jerome for Pennant, meaning the hosts had three strikers on the pitch.
Peter Crouch could not reach a Wilkinson cross while home debutant Geoff Cameron, the American international, was taking over from Rory Delap as the Potters' long throw specialist.
At the other end, Cazorla's effort was deflected wide, and from the resulting corner from the Spaniard, Olivier Giroud's acrobatic effort missed the target.
Arsenal manager Arsene Wenger sent on England wingers Alex Oxlade-Chamberlain and Theo Walcott as he desperately looked to break the deadlock.
But the goal showed no signs of coming with Arteta slicing a shot wide before Abou Diaby lost his footing in the penalty area.
Pulis opted to go on the defensive as he replaced Crouch with Ryan Shotton but Stoke then had penalty claims for a handball by Arsenal full-back Carl Jenkinson.
Arsenal came closer to that elusive goal as Oxlade-Chamberlain headed over Arteta's corner and at the other end Kightly played in Walters whose weak effort was comfortably gathered by Mannone.
Then, a minute from time, Giroud's spectacular 35-yard effort came desperately close to beating Begovic before both teams were forced to settle for a draw.
Source: AFP
Source: AFP