The visitors took the lead after just nine minutes when Charlie Adam's corner fell to Jonathan Walters. The Ireland international needed two attempts to squeeze it past Simon Mignolet after his initial header hit Danny Graham, but he eventually bundled the ball over the line.
Sunderland's chances of finding an equaliser took a big blow 10 minutes before the break when Craig Gardner was given his marching orders for a dangerous challenge on Adam, reducing the Black Cats to 10 men.
Play was disrupted briefly during the half as a fan came on to the pitch to remonstrate with the Sunderland players.
Stoke almost doubled their lead late in the half when Cameron Jerome pulled the ball back for Walters, but his shot was blocked.
Sunderland almost pulled level right on the stroke of half time when Adam Johnson fired a free kick goalwards, but it flew just past Asmir Begovic's post and the hosts were forced to go into the break behind.