That left Arsenal in fifth place in the Premier League, three points behind Manchester City in the slot directly above.
"We just have to win our games now".
There have been various protests of late from Arsenal fans calling for the manager to leave, and early on in this game a plane flew over the ground with a banner on display that read 'WENGER - OUT MEANS OUT!'
The Gunners still need Liverpool or Manchester City to drop points before they stand a chance, but Wenger's side have now regained crucial momentum and confidence ahead of their final two games against Sunderland and Everton.
"We have to show the character again", he said.
After a 2-0 loss at rivals Tottenham Hotspur last month, Arsenal looked dead and buried in pursuit of a 21st successive Champions League qualification but the Gunners have climbed to within a point of fourth-placed Liverpool.
"When I saw the reaction from Willy, I understood immediately that it was two touches", Guardiola said.
Ozil started the move with a short pass to Alexis Sanchez before darting into the area, collecting the Chilean's return pass and lifting the ball over Jack Butland.More news: Trump threatens to cancel press briefings, says Spicer 'gets beat up'
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"The most hard thing against a team like Stoke is scoring the first goal and after that we had to be efficient".
Gabriel Jesus doubled City's lead from the penalty spot, with Shinji Okazaki halving the deficit by hooking a stunning volley into the top-right corner.
"The referee was so fearless in making the decision", City manager Pep Guardiola said. "We have to do the job first and see what happens, we'll keep fighting until the end".
Monreal found himself in a strong position to steal an unlikely goal later in the first half, but his header at the post came back off the woodwork.
Third-to-last Hull will join Sunderland and Middlesbrough in being relegated if it loses at Crystal Palace on Sunday.
"Stoke have only won one of their past nine games but are still in the running for a top-half finish".
"When they scored the hand goal they made it rough".
In an nearly completely dominant first half Arsenal looked like getting the job done nice and early but with a Monreal header crashing off the post being the closest of a fair few chances, the momentum seemed to have ebbed away, but just as Stoke seemed to be on the up and enjoying some rare possession we struck.