In a game where the visitors never really sparked into life, the Gunners enjoyed lengthy spells of possession, managing to quell a Manchester United side who have been clinical of late.
Aaron Ramsey's solitary goal in the second half settled matters, though Van Persie was left frustrated not to have been awarded a first half penalty after it appeared that the Manchester United captain handled in the box to deny the Dutchman an easy chance at goal.
"At first [the referee] wasn’t sure but I asked him again after half time and he said it wasn’t a penalty. I'm sure if he sees it again he will agree with me,' said Van Persie to Sky Sports.
United had their own penalty claims too though, after goalscorer Ramsey also appeared to have handled in the box and Gael Clichy chopped down Michael Owen in the box.
Nevertheless, Van Persie felt that his team were good value for the win.
"I think we played better today, wanted it more. In the end it was a fair result," he said.
"It was all about pride today and the fans were great. It was up for us to shown some dignity and have some honour and we did that, so I’m pleased."
The result blows the Premier League title race wide open, with Chelsea now just three points behind Manchester United, with the two meeting next weekend.
With the Gunners still six points behind Manchester United with only three games remaining, it looks as if they are out of the picture, though Ramsey says what is important for the team is that they win their remaining games.
"Our target was to keep going on until the end of the season and try win all our games and see where we get from there," he said.
"We’ve done the first one today and we’ve still got a few games left and hopefully we can win them as well."