Less than two minutes later Dominik Frieser restored Barnsley's lead with a cool finish.
But Smith netted three minutes after the restart after keeper Jack Walton made a hash of a routine cross.
Defender Nathan Collins was then sent off for violent conduct for an off-the-ball incident with Frieser, but the home side managed to navigate their way through the final half an hour with a man short.
Barnsley caretaker boss Adam Murray opted for three changes to his team after a miserable start to the league season which saw the South Yorkshire side without a league win.
Simoes started alongside Frieser and new signing Callum Brittain made his club debut.
And it was Frieser who had a hand in a good early chance for the visitors. He collected skipper Alex Mowatt's pinpoint long pass and squared for Cauley Woodrow, but the striker saw his powerful volley blocked by Collins at the near post.
The opening goal was not long around the corner – and it was a moment of magic from Woodrow which provided it.
The striker bamboozled centre-back Harry Souttar with a lovely turn and duly squared the ball to Simoes to slot home into the bottom-right corner.
Stoke grew into the contest and should have equalised shortly after the hour mark, but Campbell somehow fired wide from close range after a dangerous delivery into the box by Josh Tymon.
Strike partner Steven Fletcher had an even better chance to level matters, but Walton thwarted him with an excellent low save.
Midfielder Romal Palmer tried his luck from distance as the Tykes looked to double their advantage, but his powerful left-foot strike flew wide of the target.
Stoke were level a minute before the break. Souttar made amends for his mistake with a defence-splitting pass which allowed Campbell to rifle right-footed into the bottom-right corner.
However, the Potters' joy was short-lived as Mowatt picked out Frieser with a delightful cross and the Austrian midfielder poked home to restore Barnsley's lead.
Smith was caught daydreaming as Frieser fired home unchallenged.
Smith, though, made amends for his error, powering into an open net three minutes after the restart after Walton dropped a cross into his path.
Fletcher had a good opportunity to put Stoke ahead but he blazed well over when he should have done much better in the box.
Collins was then given his marching orders for his clash with goalscorer Frieser and the hosts had to soak up the pressure.
Former Barnsley keeper Adam Davies denied Brittain with a point-blank save with quarter of an hour remaining and, just a minute later, blocked a deflected shot from the same player.
Davies held a Woodrow piledriver in stoppage time as Stoke held on for a point.