West Brom settled into the game the stronger side and Chris Brunt had the first effort on goal, but his strike from distance sailed over the bar.
Geoff Cameron found space in the box, turning inside Youssouf Mulumbu, but he blazed his shot off target on 15 minutes.
In the 25th minute Stoke came close to breaking the deadlock when an Etherington free kick almost caught out Foster, but the goalkeeper recovered to keep it out.
Both defences remained on top of proceedings and the sides went in level at 0-0 at the break.
There seemed little urgency for either side to break the deadlock with West Brom looking comfortable on the ball and Stoke sitting deep.
The visitors were looking more likely to get that crucial goal, but Lukaku put a good chance wide after being played in by Brunt.
Mulumbu tried to find the corner with a curled effort from the edge of the box but despite his effort beating Begovic, it went just wide.
Despite their huffing and puffing, the visitors could not create the big chance needed and had to settle for a point.