Gunners boss Arsene Wenger wanted to rest his top-scorer for the Premier League clash at the Emirates Stadium, but he was forced to turn to the Dutch forward after Peter Crouch had cancelled out Gervinho’s opener.
Van Persie was introduced midway through the second half and netted shortly afterwards.
His second strike came seven minutes from full-time to make sure of a third win for Wenger’s team within a week and lift Arsenal into seventh place.
Wenger’s side had struggled to create chances without Van Persie leading the attack.
Marouane Chamakh stepped in for Van Persie and the closest he came in the early stages was heading wide from Mikel Arteta’s corner.
Arteta also drove wide from 25 yards and Aaron Ramsey was off-target with an effort from a similar distance before the hosts went ahead with their first genuine chance of the match.
The move for the 27th minute opener started on the edge of the penalty area when Ryan Shawcross tackled Theo Walcott, with the ball breaking for Ramsey.
Ramsey lobbed his pass over the Stoke defence and Ivory Coast forward Gervinho, who had remained onside, had time to control with his chest before planting his finish beyond Asmir Begovic for his second goal since arriving from French club Lille.
Stoke, however, showed their battling qualities to get back in the game, although Dean Whitehead’s efforts earned a yellow card when he crashed into Arteta for a second time in the match.
They were level in the 34th minute when Arsenal showed their familiar weakness of failing to deal with set-pieces, althoug they were upset at Laurent Koscielny being penalised for a foul on Crouch.
Glenn Whelan floated the resulting free-kick down the right channel, Shawcross headed across goal and, after a goalmouth scramble, Crouch flicked the ball in after Jonathan Walters had nodded towards goal.
It was Crouch’s third goal in five matches and it led to Arsenal fans growing restless.
The hosts thought they should have had a penalty straight after the equaliser when Andy Wilkinson appeared to wrestle with Chamakh, but referee Lee Mason waved play on.
Wilkinson was given a yellow card in the second half when he fouled Walcott but chances were proving difficult to create, with Stoke bringing on Salif Diao for Rory Delap to give a more defensive look to their midfield.
Van Persie was brought on in the 66th minute in an attempt to change the game and he was immediately in the action.
The 28-year-old created a chance but his cross was too high for Laurent Koscielny. He also accused Shawcross of elbowing him in an aerial challenge.
It took him just nine minutes to get on the scoresheet for his eighth of the season, with the move started by Arteta floating the ball out to Gervinho on the right.
Gervinho powered into the penalty area and pulled the ball back for Van Persie, whose finish wrong-footed Begovic and crept into the near post.
Gervinho also set up Van Persie’s second, this time pulling the ball back from the left and Begovic again getting his hands to the finish but failing to prevent it crossing the line.