The new signing struck two minutes after the break and the Potters were able to deal with frequent pressure from Arsenal to keep a clean sheet and get their first win on the board this campaign.
Stoke boss Mark Hughes handed a first appearance to Paris Saint-Germain loanee Jese and the Spaniard almost netted a dream opener as he flicked the ball over Shkodran Mustafi's leg before forcing a save out of Petr Cech from an acute angle.
It took a while for Arsenal to impose themselves on the match but on 17 minutes, Jack Butland denied Aaron Ramsey with a smart stop down to his left after the midfielder had run onto a pass from Alexandre Lacazette.
Moments later, Danny Welbeck connected well with a half-volley, only to see Butland stay strong at his near post, before up the other end, Eric Maxim Choupo-Moting miscued a first-time strike after more positive work from Jese.
Arsenal responded with a superb floated delivery from Alex Oxlade-Chamberlain which found the run of Ramsey at the back post but again, Butland made himself big at his near post to keep his side on level terms.
Shortly after the half-hour mark, Stoke should have opened the scoring when Choupo-Moting found Ryan Shawcross all on his own by the penalty spot, but the Potters skipper directed his free header marginally high and wide of Cech's post.
Two minutes into the second half, the Potters did go in front through Jese, who started a move also involving Saido Berahino before firing a low strike into the bottom corner from 12 yards.
From then onwards, Stoke instead opted to sit deep and invite pressure from the visitors and it only led to a succession of chances for Arsene Wenger's side.
Hector Bellerin had a shot smothered by Butland, while Welbeck directed the ball over the bar with his shoulder from 12 yards, before up the other end, Berahino saw a header tipped over by Cech as the wait for his first Stoke goal continued.
Back came Arsenal, with Welbeck's poked effort being blocked by Butland before Mesut Ozil sent a left-footed curler from 25 yards wide of the far post.
Arsenal's Lacazette had the ball in the net with a sharp finish from inside the penalty area but despite appearing to be level, the Frenchman was adjudged to be offside by the assistant.
All of the pressure in the closing stages continued to come from Arsenal but despite Wenger making changes to his frontline, the North Londoners were struggling to create any more clear-cut chances.
In the fourth minute of added-on time, Olivier Giroud was provided with a header inside the penalty area but although he got the better of Shawcross, he powered his effort wide of the far post.
It proved to be Arsenal's final opportunity and it capped a frustrating 90 minutes for Wenger and his players who already concede ground to Manchester United - and potentially some of their other rivals - in the race for the league title.