The Gunners opened the scoring away at Stoke for the first time ever in a Premier League encounter when Olivier Giroud tapped in before the break after a dominant first-half.
After the break Mesut Özil combined brilliantly with Alexis Sánchez to put Arsenal 2-0 up at the bet365 Stadium before Stoke substitute Peter Crouch pulled one back on 67 minutes with a controversial handball goal.
But two quick-fire goals from Sánchez - despite evidently carrying a thigh injury - and Giroud, his second of the game, put Arsenal back in control to claim a deserved three points and put the pressure on fourth-placed Liverpool.
The North London outfit are only a point behind the Reds, who can restore their four-point advantage if they beat West Ham United at the London Stadium on Sunday.
Koscielny and Giroud among four Arsenal changes
Arsène Wenger made four changes to the team that beat Southampton on Wednesday night, keeping the 3-4-2-1 formation as Laurent Koscielny returned from a calf injury, pushing Nacho Monreal to left wing-back.
Alex Oxlade-Chamberlain missed out with a calf injury of his own, allowing Hector Bellerín to return on the right, while Francis Coquelin and Giroud came back in.
The home side made only a single change from a 2-2 draw at Bournemouth last Saturday, Erik Pieters replacing Marc Muniesa at left-back. Mame Biram Diouf remained up front after netting against the Cherries.
Arsenal controlled all of the early stages, Jack Butland forced into a good save on eight minutes when Shkodran Mustafi met Özil's near-post corner to send a looping header that the 'keeper stretched to tip over his crossbar.
Butland should have been tested again quickly after when Özil's precise pass over the top found Monreal - who sneaked into space behind Glen Johnson - but the Spaniard's poor control allowed the ball to run out of play.
Giroud taps in to reward Gunners' dominant first-half performance
Monreal crashed the post on 16 minutes when Ryan Shawcross flicked Bellerín's cross into the Spaniard at a nice height at the back post but he could only hit the woodwork, while Özil's follow-up was blocked.
Stoke lacked any particular tactical blueprint and had few chances, Marko Arnautović curling a free-kick over the bar after Mustafi had hacked down Xherdan Shaqiri 20 yards from goal.
Arsenal largely struggled to fashion real chances to test Butland, Sánchez firing into the side-netting after Giroud had pressured Johnson into coughing up possession.
But the breakthrough came on 42 minutes when Coquelin found Bellerín on the overlap down the right and the wing-back rolled a cross into the six-yard box for Giroud to tap in with his just his 11th touch of the afternoon.
Özil doubles Arsenal's advantage before Crouch pulls one back off the bench
After a quiet first 10 minutes of the second-half, Özil doubled Arsenal's advantage thanks to some sublime link-up with Sánchez.
The pair demonstrated exactly why the club should be doing their all to pen them to new contracts, a one-two seeing the Chilean thread a sublime through ball for Özil to clip beyond Butland into the far corner.
Stoke almost pulled one back before the hour mark when Arnautović did well to reach the by-line, but his cross was slightly behind Diouf inside the area and the striker could somehow only guide his header wide from point-blank range.
That was his final touch as Hughes threw on Saido Berahino and Crouch and Stoke ramped up the pressure with their new introductions, Cech needing to push a Bruno Martins Indi header over the bar from a corner.
But their newfound energy was rewarded with a goal on 67 minutes, though one which should not have stood. Arnautović beat Monreal to break into the box on the left and found Crouch - who threw his head towards the ball but connected with his hand - to reduce the deficit to one goal.
Wenger rightly protested on the sidelines and the intensity of the game soared as much as the atmosphere within a thunderous bet365, but Arsenal's two-goal lead was restored with 15 minutes to go to quell hopes of a comeback.
Sánchez and Giroud put away side out of sight
Stoke has been a difficult away game for Arsenal over the years but they overcame Stoke's spell and Sánchez - who had appeared to gesture to the Arsenal bench that he needed taking off as he limped around with a thigh problem - fired in the visitors' third courtesy of a Shawcross deflection.
Receiving the ball from Bellerín on the edge of the box, Sánchez moved into space and fired towards the far corner on his left foot - his shot taking a nick off Shawcross' calf to beat Butland.
That goal was his 50th Premier League goal in 101 appearances and meant only Ian Wright and Thierry Henry had reached that landmark quicker in the Premier League era for Arsenal.
It was Sánchez's final contribution, though, as Wenger brought him off straight after. And yet Arsenal scored a fourth to pile further misery on Stoke - who have conceded four goals on seven occasions this season - as Giroud netted a brace.
Substitute Aaron Ramsey forced a good low save from Butland moments earlier but he broke away from Johnson inside the box and swung a cross that Giroud slid in to finish, making it 4-1 with his 12th league goal of the season.
The home end emptied rapidly and Cech was forced to deny Geoff Cameron's drive, but Arsenal maintained a thoroughly one-sided score-line as they claimed their fifth win within their last six games.
Arsenal now face Sunderland and Everton, both at home, in their final two games next week.
However they still need West Ham or Middlesbrough to do them a favour if they are to leapfrog Liverpool and qualify for the Champions League for the 21st consecutive campaign.
Stoke remain on 41 points from 37 games, having never finished with less than 42 points in a Premier League season. They travel to mid-table Southampton on the final day next Sunday.