The Gunners closed the gap on their rivals to seven points after a stunning comeback from two goals down.
Van Persie scored the equaliser just before half-time, and though Szczesny insists that the contract talks aren't his business, he believes the striker will extend his stay in north London.
"We really don't discuss [speculation], it is not our business," Szczesny told talkSPORT. "We just want to have him at the club.
"We are trying to make the most of it while he is here, he is a great captain and leader of the team and we are very pleased to have him.
"I'm personally confident that he will stay at Arsenal. That is where he belongs and that is where he is at his very best.
"Robin does his talking on the pitch by scoring all the goals for this club and I think that shows you his commitment. We are confident he will be staying at Arsenal."
The goalkeeper admitted that the victory over Spurs was one of the best moments in his career, and that he hoped it could transform their season - but admitted they cannot realistically win the title.
"I hope [the result has a psychological effect on Tottenham] as an Arsenal fan," Szczesny told the Evening Standard. "I said ages ago we can't realistically win the Premier League but now my main ambtition is to finish above Spurs.
"You can see we are no worse than them and when we have the momentum and are on the front foot, we are dangerous. I hope we use that again to our advantage and get the momentum to start challenging for the first spot.
"[The feeling] is comparable to that of beating Barcelona. It is great, probably one of the best I have ever had. I hope it can transform our season.
"In the last two games at home, we have scored 12 goals. It just shows you what we can do when we are on the front foot and we can really go for it. Hopefully we can learn from that and repeat it all over again.
"Every single goal felt better than the previous one and I was celebrating quite energetically. But I loved it. It is the firs ttime I have beaten Spurs and it is just great."