Odemwingie struck in the 62nd minute, firing in from the edge of the box after collecting the ball from a stray Ahmed Elmohamady pass to register his fourth goal in three games, and fifth since joining the Potters from Cardiff in January.
Stoke boss Mark Hughes said: "It's another landmark point of the season for us - 40 points always figures in people's minds before the season starts.
"But certainly we set targets at the beginning of the season that we hoped we'd be capable of and now it looks like we've got a real chance of achieving something that a Stoke side hasn't done this year.
"So we've just got to keep going - we've got six games left, we've got good opportunities, certainly here against teams that we feel we can go well against - so further opportunities obviously to put more points on the board.
"Today was important, we didn't really hit the heights we have done in recent weeks, but it was a good three points anyway."