Sebastien Squillaci's eighth-minute header gave Arsenal the victory but injuries to Theo Walcott and Cesc Fabregas will be of concern with the Carling Cup final and a Champions League match against Barcelona coming up.
Fabregas came off with what appeared to be a knee complaint in the first half while Walcott was carried off on a stretcher with an ankle injury after a Dean Whitehead challenge, which went unpunished.
Much of the pre-match talk had been about how the Gunners would cope without another of their key men, Robin van Persie, who was ruled out on Tuesday with a hamstring injury.
Arsene Wenger chose Nicklas Bendtner to lead the attack in his absence while Fabregas, Wojciech Szczesny and Samir Nasri returned after missing Sunday's disappointing draw with Leyton Orient.
Tony Pulis recalled Asmir Begovic and Whitehead while Ryan Shawcross skippered the side almost a year to the day the that his challenge led to Aaron Ramsey's broken leg at the Britannia Stadium.
Clearly determined to put their shock FA Cup draw behind them, Arsenal came flying out of the blocks and rattled the Stoke woodwork with barely a minute gone.
Fabregas slotted in Walcott after some good work by Jack Wilshere, and the England winger beat Begovic at the far post but saw his shot rebound off the woodwork and into the goalkeeper's hands.
Walcott tore into the Stoke box again three minutes later after being played through by Bendtner but Begovic came out to smother the ball.
The early pressure paid off for the home side when they took the lead in the eighth minute. Bendtner volleyed across the box from a Wilshere corner to find Squillaci, who headed home unmarked from five yards for his first league goal of the season.
However, Arsenal suffered a blow 14 minutes in when Fabregas, who looked to be struggling with a knee injury, asked to be withdrawn. He was replaced by Andrey Arshavin.
Fabregas, who missed most of December with a hamstring injury, will be badly missed by the Gunners if does not recover for Sunday's cup final and the Barcelona game in two weeks' time.
Arsenal remained in control for much of the first half but played the game at a much slower pace following their captain's departure.
Arshavin, who scored the winner against Barcelona last week, skipped past his marker before drawing a good save from Begovic at his near post but it was Szczesny making the stop of the game at the other end when he had to scramble down to his right to save John Carew's 25-yard volley.
Nasri curled a free-kick a couple of yards wide of Begovic's goal after Shawcross had brought down Arshavin 20 yards out before the first booking was shown on Jonathan Walters for a pull on Walcott.
The decision angered Pulis and his players, who had just seen Squillaci go unpunished for a similar challenge.
Stoke almost equalised at the start of the second half when Shawcross' header was deflected just wide by Djourou after Jermaine Pennant had crossed from Delap's short throw.
Stoke were looking much more threatening than they had done in the first half and they went close again when Robert Huth headed just over the bar from a Delap long throw this time.
However Arsenal then went on the attack through Arshavin, who dodged a Shawcross sliding tackle to find Walcott in the box, but the 21-year-old was off-balance and mis-kicked his attempt on goal under pressure from Huth.
Walcott was bundled over by Whitehead on the edge of box in the 68th minute but referee Peter Walton waved play on. However, the winger stayed on the ground, clutching his ankle, before being carried off to be replaced by Denilson.
Bendtner headed wide from six yards after a Wilshere corner as Arsenal looked for a killer second goal with 20 minutes left but Pennant almost stole an equaliser in the last minute of normal time with a beautiful curling free-kick that went into Szczesny's side-netting.
Wenger was infuriated to see the fourth official show there would be five minutes of injury-time but his side held the ball for almost the entire added period to ensure the Gunners held out for a crucial win.