The Gunners were unable to breach the Sunderland defence last week and it was a similar story in the Potteries with Tony Pulis' side able to snuff out any forward advances.
As usual, Arsene Wenger's side had the lion's share of possession but could not put that on the scoresheet as their new strikers Lukas Podolski and Olivier Giroud failed to link up together.
In the seventh minute, Stoke haddisallowed goal when Jon Walters fired home from Peter Crouch's glancing header but the flag was up for offside.
Moments later, Podolski was unlucky not to score when Andy Wilkinson fell into his path as he shot with the Gunners also unlucky not to be awarded a penalty for handball although there were no protests from the visitors.
On the half-hour mark, Michael Kightly stung the palms of Vito Mannone, who was in for the injured Wojciech Szczesny, minutes before Santi Cazorla pulled the trigger from about 25 yards but Asmir Begovic was up to the task.
Kieran Gibbs tussled with Jermaine Pennant right on the edge of the area but referee Lee Mason waved away the protest.
Both sides lifted the tempo late in the search for a winner with the closest chance coming through Giroud who had an outrageous effort on his left foot from an angle very late in the match which had Begovic scrambling.
In the end though, it was a stalemate between the Gunners and Potters with the former failing to score in two outings whilst the latter now has two points following their opening weekend draw at Reading.
Britannia Stadium, Stoke-on-Trent - 27,072