Although a dire first-half performance did pick up after the restart, Bolton barely resembled the team which had bossed Derby in such impressive fashion a few days earlier.
Bruno Martins Indi took advantage of some sloppy defending to open the scoring 10 minutes in with Tom Ince capping a fine individual performance with the Potters’ second 16 minutes before the end.
Wanderers may point to a Josh Magennis goal ruled out midway through the second half, which would have levelled the scores.
But there can be little argument that Stoke deserved only their third victory in 11 attempts this season.
Parkinson had made just one change to the team, taking out David Wheater and bringing ex-Potteries man Marc Wilson back after a one-game suspension.
The starting line-up contained nine summer signings, with just four of the match-day squad involved in last season’s Championship great escape.
Wanderers had not conceded a goal in just over three hours of football but Martins Indi changed all that with a header of puzzling ease direct from a corner.
Remi Matthews had pushed aside a stinging shot from Tom Ince to give his side some temporary respite from the pressure.
But when the cross came in, Indi’s marker – which appeared to be Hobbs – was nowhere to be seen and the Portuguese defender had the freedom of the Potteries to head into the net.
Oddly, Bolton may have already been a goal to the good.
In the opening few minutes Will Buckley put in a fine cross for Josh Magennis only for a slight deflection to put the Northern Irishman off-balance and his shot over the bar.
Once Stoke had taken the lead, however, there was no let-up in the pressure.
Afobe scooped a shot over the top from close range and Bojan was denied by a terrific block by Wanderers captain-for-the-night Jason Lowe.
Matthews also blocked an effort from Saido Berahino at his near post as Stoke spent a full half-hour camped out in Bolton territory without managing to find a second goal.
On the rare occasion Wanderers did manage to break into the home half, some dithering decision-making and dreadful pass execution left Gary Rowett’s side with very little to trouble them.
On Saturday Wanderers had given Derby the vast majority of possession but looked compact and a danger on the break.
Here, there were worrying gaps exploited by Ince and Bojan on a regular basis, while the attacking threat was virtually non-existent for the opening 45 minutes.
Parkinson had asked his players to stick to the game-plan.
But while Stoke had a list of Premier League class players at their disposal, it was hard to shake the feeling they were being made to look a better side by Bolton’s obvious disjointedness.
Wanderers flickered into life at the start of the second half as Joe Williams and Craig Noone conspired to send a decent ball in to Magennis – but Stoke cleared and then very nearly grabbed a second on the counter when Ince exploited the acres of space ahead of him.
Noone had a first shot on target for Wanderers on 55 minutes, cutting in on his left foot from the right wing. His effort was celebrated with some irony by the travelling fans, whose boisterous chants continued at full volume regardless of what was being served up before them.
A first corner of the game then served up a real talking point. Ashley Williams and Josh Magennis wrestled for a full 30 seconds before Erhun Oztumer whipped the ball to the far post – but only after Magennis had nodded the ball over the line did referee Jeremy Simpson rule a foul.
Oztumer and Joe Williams added more of a sense of urgency after the break, the former driving a shot into the side netting to give some hope going into the closing stages.
Parkinson threw on Christian Doidge and Clayton Donaldson thinking the same but moments after they had arrived on the pitch, Ince killed the contest off.
Collecting James McClean’s cross on the edge of the box, the Stoke winger beat Jonathan Grounds and then recovered from a slip in time to angle his shot under Wilson’s challenge and into the bottom corner.
It might have been three – Pawel Olkowski cleared Ince’s cross over his own bar and Indi got space to put another header in on goal, this time angled wide.
As the old footballing cliché goes, the yardstick of any side is whether they can do it on a wet and windy Tuesday night in Stoke.
Sadly, the answer on this occasion for Wanderers was an emphatic ‘no.’
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