On what was a disappointing night for the Baggies, the hosts saw Sam Surridge miss a penalty while they also wasted numerous other goalscoring opportunities.
In contrast, Albion created very little with their only clear chance falling for skipper Jake Livermore who prodded wide from close range.
After Surridge's penalty miss - in the 71st minute - it felt as if it would be one of those days where it just wouldn't go in for Stoke.
But eventually, they did get the breakthrough thanks to a smart finish from Nick Powell.
And that proved enough to earn a deserved three points for Michael O'Neill's side.
Following their impressive performance at Cardiff, Ismael opted to name an unchanged team for the short trip to Stoke.
Sticking with his 3-4-3 formation, Jordan Hugill operated as Albion's central striker with Callum Robinson on the right flank and Karlan Grant on the left.
In the back three, Conor Townsend continued to partner Kyle Bartley and Semi Ajayi with Darnell Furlong and Adam Reach at wing-back.
Stoke, who included former Albion centre-back James Chester in defence, liked up in a 3-4-2-1 system.
It saw Nick Powell and Mario Vrancic operate just behind lone striker Jacob Brown with Tommy Smith at right wing-back and Josh Tymon on the left.
It was the Baggies who started the game the brighter of the two team's with Ismael's men setting traps and consistently winning the ball high.
But in the 10th minute, Stoke really should have gone ahead when Townsend's slip allowed the hosts to exploit Albion's high line and send Brown clean through on goal.
The striker had plenty of time to decide what he was going to do.
But he only succeeded in smashing the ball against the base of Sam Johnstone's post. In the second phase, Joe Allen then fizzed a strike from 18 yards narrowly past the post.
Overall, the game was proving an open and entertaining affair.
And Stoke came close to breaking the deadlock once again when a clever reverse-pass got Tymon in behind the defence.
On the edge of the six-yard-box, the wing-back managed to get this shot away.
But he was denied by Johnstone who raced off his line to make an impressive block.
Albion responded with Robinson have three shots inside the box in quick succession - with two blocked and the third claimed by goalkeeper Adam Davies.
Following that blistering start, the game settled down as the clock ticked past the half-hour mark with the two sides cancelling each other out.
It was Stoke, though, who were playing the better football.
And in the 41st minute they were denied what looked to be a clear goal with a controversial refereeing decision from Tim Robinson.
Vranicic looked to win the ball high up the pitch and in doing so looped it into the box but also caught Callum Robinson.
Furlong then looked to have a simple header back to Johnstone.
But he only succeeded in heading the ball past his keeper for a hugely embarrassing own-goal.
The wing-back looked distraught.
But fortunately for Albion, referee Tim Robinson pulled play back after deeming Vrancic had fouled Callum Robinson when winning the ball.
Stoke came close again shortly after the re-start with Vrancic clipping the top of the crossbar with a free-kick from just outside the box.
Albion had struggled to make the ball stick up top all evening.
So it was no surprise when Ismael introduced Matt Phillips for Hugill early in the second half with Grady Diangana then replacing Grant shortly after.
With 25 minutes to go, the game was there to be won for either side.
And that was shown in a frantic 60 second spell within which both teams should have scored.
It was Stoke who created the first chance with Tymon sending in a low cross that substitute Sam Surridge looked destined to side-foot home inside the six-yard box.
Somehow, though, Johnstone managed to get down and spectacularly keep the ball out.
The Baggies went straight up the other end where Furlong launched a long throw into the box.
And that eventually fell for Jake Livermore who, just yards from goal, stabbed the ball wide when he really should have scored.
If that wasn't dramatic enough, Stoke were then awarded a penalty after Johnstone bundled Surridge over in the box.
The striker dusted himself down to take the spot-kick himself.
But Johnstone atoned for his error by producing a strong arm to keep the ball out.
All Stoke fans inside the stadium were at a loss as to how their team wasn't ahead.
But with 10 minutes to go they did get the goal they deserved when Townsend sent a clearance straight to the feet of Smith.
He then produced a bit of quality to lift the ball over Albion's defence.
And that was met by Powell who looped the ball over Johnstone and into the net.
Albion increased their attacking threat from that point and looked most likely to pinch an equaliser from a set-piece.
But it wasn't to be with Stoke coming away fully deserving of the points.
Stoke (3-4-2-1): Davies, Wilmot, Souttar, Chester, Smith, Allen, Thompson, Vrancic (Fletcher 76), Tymon, Powell (Doughty 87), Brown (Surridge 57).
Subs not used: Bursik, Batth, Ostigard, Ince.
Albion (3-4-3): Johnstone, Ajayi, Bartley, Townsend, Furlong, Livermore, Mowatt (Molumby 80), Reach, Robinson, Hugill (Phillips 55), Grant (Diangana 57).
Subs not used: Button, Kipre, Bryan, Clarke.