Germany international Mesut Ozil turned in an outstanding first-half display at the Stadium of Light as the Gunners claimed a win, although in controversial circumstances.
Theo Walcott wasted two glorious opportunities, both of them set up by Ozil, to beat keeper Keiren Westwood and then headed wide from Giroud's cross with Sunderland, who had earlier hit the bar through Modibo Diakite, in disarray.
However, half-time substitute Craig Gardner dragged the home side back into it with a 49th-minute penalty after Adam Johnson had been tripped by Laurent Koscielny, and the visitors found themselves on the back foot for the first time.
Aaron Ramsey volleyed Wenger's men into the lead with 67 minutes gone and then sealed the win nine minutes later, but not before referee Martin Atkinson had intervened.
However, Mr Atkinson had already blown for a foul by the defender, who was then only booked as the home crowd howled for a red card.
Di Canio, who was sent to the stands after complaining to the official about Giroud's dawdle from the pitch when he was substituted in injury time, said: "It was a mistake.
"The referee has the power to wait to see how the action finishes, and then he can come back to his decision.
"They have to wait. It's not Paolo Di Canio, it's the rule, so he made a mistake because he stopped the game early, especially in the balance of the action.
"You could see Altidore is much more powerful than Sagna, he was shielding the ball well. It was clear he was near to winning the challenge.
"That was a key moment because we can't imagine that we would have many more opportunities to score, so that decided the outcome of the game.
"That can happen. He is a man. It's important that he accepts this - I make mistakes every single moment when I make decisions with my players; my players make mistakes in front of goal."