Arsene Wenger's decision to start his captain on the bench almost backfired as they only had Gervinho's strike to show for their dominance in the first half.
To add to their problems, former Tottenham striker Peter Crouch marked his return to north London with an equaliser 10 minutes before the interval.
With the Gunners labouring against their battle-hardened visitors, Van Persie was let loose with 25 minutes remaining.
And within a quarter of an hour he had scored twice to bail out his shot-shy team-mates and take his goal tally to a remarkable 29 in his last 34 appearances for the club.
It was hardly a convincing performance from Arsenal, and yet a sixth win in their last seven matches is not exactly the record of a club supposedly in crisis not so long ago.
In van Persie's absence, Marouane Chamakh got a chance to impress, and he should have given Arsenal the lead in the 10th minute with a free header from Mikel Arteta's corner but made a mess of his effort which flew wide.
Mikel Arteta fired a low drive narrowly wide and Gervinho just failed to control Aaron Ramsey's lofted ball into the area as the hosts warmed to their task.
In the 23rd minute Ramsey almost repeated his midweek heroics in Marseille with a fierce drive which fizzed just wide.
The goal Arsenal had been threatening arrived in the 27th minute, with Ramsey the architect.
The Wales international, who had his leg broken by Stoke's Ryan Shawcross 18 months ago, collected a half-clearance from the Potters defender and chipped it back into the area.
Gervinho's chest control this time was perfect, creating the angle for him to beat the diving Asmir Begovic from 12 yards for his second goal since joining the club.
But Stoke grabbed a shock leveller seven minutes later from a disputed free-kick after Laurent Koscielny was adjudged to have fouled Crouch.
As Wenger protested to fourth official Jon Moss, Glenn Whelan lofted the ball into the area, Shawcross' cross found its way to Jon Walters at the far post and his header back across goal was nodded in by Crouch.
Arsenal began the second half sluggishly, with the biggest stir caused by van Persie when he began to warm up on the touchline.
Chamakh passed up another half-chance with an overhead kick which drifted wide following a goalmouth scramble.
The change was inevitable and van Persie finally made his entrance with 25 minutes remaining, replacing Chamakh.
The Dutchman almost made an immediate impact with a neat turn and a cross which flew just over the head of Ramsey.
But it took only eight minutes for the new arrival to get Arsenal back on track.
Gervinho beat Walters to reach the byline and pulled the ball back for new strike partner van Persie, who squeezed the ball between Begovic and his near post.
And van Persie had the final say with six minutes to go, Gervinho again the provider with a low cross which the in-form Holland star fired past Begovic to kill Stoke off.