In his first game in charge of The Potters, the Northern Ireland manager - who is continuing to take control of his national team’s Euro 2020 qualifying campaign - oversaw a comfortable victory that piled significant pressure on Barnsley and their caretaker manager, Adam Murray.
Murray’s chances of getting the Reds’ job permanently - raised by impressive displays in recent weeks, if not quite the wins he is seeking - were damaged by a largely powder-puff performance.
Although there was plenty of endeavour from his embattled team, there was precious little of the quality that will be needed to get out of trouble, and although only one place and one point separated the sides before start of play, they have the look of clubs on opposite trajectories.
When you are fighting for your life at the wrong end of the table, the last thing that you need is for your opponents to open the scoring with a wonder goal from pretty much the halfway line.
Sam Clucas, the Stoke City midfielder, was actually just inside the Barnsley half when he did Brad Collins with an outrageous lob in the eighth minute, pinging back a clearance from the goalkeeper who was left stranded yards off his line.
Clucas followed up with another superb strike in the second half that put the finishing touches on Stoke’s red-letter day with their fourth goal in the 67th minute.
Teed up by Lee Gregory, Clucas let aim left-footed from fully 25 yards out, giving Collins no chance as the ball flew past his left hand and into the corner of the net in front of the 2,600 visiting fans, who created a cacophony of noise from first whistle to last.
In between times, Gregory had put Stoke 2-0 in front from the penalty spot in the 30th minute, sliding coolly to Collins’s right after Alex Mowatt tripped James McClean.
And after Barnsley had pulled one back two minutes into the second half, Cameron McGeehan driving left-footed past Jack Butland’s left-hand into the top corner from around 10 yards, Joe Allen had made it 3-1 to the visitors with a swivelled close-range finish with his right foot following a scramble from a corner.
Barnsley further reduced the deficit in the 84th minute, substitute Patrick Schmidt latching on to a through ball from Mowatt and driving past a horribly exposed Butland, but it was too little too late.
In truth, Stoke, who showed six changes from the team that lost 2-0 to West Brom last Monday, could have scored further goals.
Tom Ince had a couple of presentable opportunities, to which Collins was equal in the Barnsley goal, and some of the defending at both ends was last-ditch at times.
Barnsley had several penalty appeals - one in the 57th minute when substitute Luke Thomas appeared to be brought down by Stephen Ward as he cut inside looked convincing - but Stoke were full value for a priceless win.
Barnsley: Collins, Dougall, Diaby, Brown, McGeehan (Wilks), Woodrow, Chaplin (Schmidt 82), Cavare, Sibbick (Thomas 45), Halme, Mowatt. Unused subs: Radlinger, Andersen, Oduor, Simoes.
Stoke City: Butland, Edwards, Ward, Allen, Batth, Ince (Diouf 82), McClean, Martins Indi, Gregory (Vokes 90), Clucas (Ndiaye 73), Woods. Unused subs: Federici, Carter-Vickers, Powell, Campbell.