The Potters enjoyed the best of the first half, coming close through triallist Sebastian Boenisch, who saw his shot tipped over the crossbar.
The second half started with Yeovil in the ascendancy, however, and they were awarded a penalty just four minutes after the restart when Ryan Shawcross brought down Byron Webster. Reuben Reid stepped up and made no mistake, giving his side the lead.
They wouldn't have to wait long for the equaliser, however, as Boenisch's cross was met by the head of Kenwyne Jones to make it 1-1. Stoke pushed on to try to find a winner, but couldn't find a way through the stubborn Yeovil defence.
Stoke's first competitive match of the season comes against Reading in the Premier League on August 18.