The Dutchman had gone 10 domestic games without a goal, but he won and converted a penalty midway through the second half to make the points secure at the Britannia Stadium after Michael Carrick had opened the scoring.
He sprinted down the touchline after slotting the spot-kick past Asmir Begovic and headed straight for Sir Alex Ferguson for a big hug.
"It was an important point in the game. I had to score that one and thankfully it went in, so after that the relief of a couple of weeks came out," he told Sky Sports.
"I wanted to celebrate it with everyone, with the players, with the staff, all the players involved even on the bench because they have been great with me from day one.
"Even when it was sometimes a little bit harder they still believed in me and they still support me and help me wherever they can, so that's why I wanted to join them."
Meanwhile, man of the match Wayne Rooney, who played in a midfield role, said he hoped Van Persie can help fire United to the title.
"As a football player, as a striker and a goalscorer, you think every player in the world has had a few games in a row where they weren't scoring," he said.
"Robin's kept his head down, he's worked hard and thankfully today he's got his goal. Hopefully that'll kick him on because he'll be a massive player in the next few games for us."