Ireland could have increased West Brom's ire moments later but blazed over while Stephane Sessegnon could have won it in the last minute when he shot at Asmir Begovic after beating the defence.
Despite that a draw was perhaps a fair result for a game that failed to spark, aside from the occasional flashes of excellence from players such as Sessegnon, Ireland and Marko Arnautovic.
The result meant goal-shy Stoke have still only struck the net four times this season.
The first half lacked major incident although the visitors, with Sessegnon looking lively, made a promising start.
Sessegnon weaved his way through the Stoke box early on but the hard-working Steven Nzonzi got back to end his charge.
Sessegnon flashed a snap-shot wide and then almost broke through when he jinked past two tackles after good work by Victor Anichebe and Saido Berahino, but Begovic blocked.
Begovic, showing no signs of weariness after an eventful week in which he helped Bosnia qualify for the World Cup, then needed to be alert to deny Morgan Amalfitano.
Sessegnon was again at the heart of the attack and could have shot before laying off to Amalfitano, but Begovic rushed out to smother the Frenchman's shot.
Stoke realised they needed to cut out the supply to Sessegnon and, with Nzonzi busy in their midfield, they came into the game more.
Jonathan Walters had a long-range effort easily saved by Boaz Myhill and Adam headed well over from a corner.
A clever free-kick by Arnautovic, played low to Ireland as West Brom lined up expecting a cross, almost paid off but Myhill cut out the Irishman's ball across goal.
The fare improved little after the break and the frustration of both sides was perhaps evident in the increased number of fouls.
Adam was perhaps fortunate to escape punishment for catching Sessegnon on the ankle in an incident by the touchline.
The Scot got even luckier 10 minutes into the second half when he clipped the heel of Mulumbu in the area.
Referee Howard Webb was unmoved, and Mulumbu's theatrical fall and disbelieving reaction may not have helped his cause, but replays did suggest a penalty should have been awarded.
Adam almost rubbed salt into West Brom's wounds moments later with a fine ball to release Arnautovic into space down the right.
The Austrian picked out Ireland with a superb ball but the midfielder put his first-time shot and a glorious chance over the bar.
Adam, as if energised by his reprieve, started to dictate the pace of the game.
He even almost caught out Myhill from the halfway line as play broke up but the Wales goalkeeper scrambled back to palm over his spectacular opportunistic effort.
Despite that, Adam continued to tread a fine line and manager Mark Hughes decided to replace him after he bundled over Billy Jones to halt a West Brom attack.
West Brom tried to change the flow by sending on Nicolas Anelka and Shane Long in attack but Stoke continued to press better.
Ireland almost turned provider for Arnautovic but the Austrian was inches away from sliding onto his ball.
Sessegnon attempted to test Begovic with a powerful 25-yard shot but the goalkeeper was not troubled.
Sessgenon almost grabbed a brilliant winner in the last minute when he weaved his way through the Stoke area but, with just Begovic to beat, he shot into the keeper's midriff.