The winger reacted quickest from Asmir Begovic's spilled save from Fabio Borini's shot to turn it home after 17 minutes.
Steven N'Zonzi was sent off for two bookable offences on Jozy Altidore as the Black Cats survived a late rally from the Potters.
See how the action unfolded below.
"The reason Sunderland stayed up [last season] was because Cattermole was injured and Bardsley played very little."
STOKE: Begovic; Cameron, Shawcross, Wilson, Pieters; Odemwingie, Nzonzi, Adam, Whelan, Assaidi; Crouch