Van Persie had gone 10 domestic games without scoring but won and then converted a penalty in the 66th minute to make it 2-0 to United at the Britannia Stadium after Michael Carrick had opened the scoring from a corner inside four minutes.
Van Persie ran to the touchline and heartily embraced Ferguson after finding the bottom corner, and the Scot joked: "He nearly killed me! He forgets I'm 71.
"It was a great celebration as it brought the emotion of the players and the fans together. We really did celebrate that."
Van Persie had seemed unstoppable following his move from Arsenal to United last summer and scored 23 goals in his first 31 games for the club. But the goals have dried up in the past two months and Van Persie had not scored for United since a 2-0 victory over Everton on February 10.
Ferguson told Sky Sports: "For all strikers, and I was one myself, you go through spells when you are not scoring and thinking you will never get a goal. Then, when you are scoring, you never think you are going to miss.
"It was an important goal and there were two or three things about it. He did really good work from Wayne's pass to get the penalty. Then the ball moved off the spot two or three times (in the strong wind) and he showed composure to settle himself down and score a perfect penalty."
Ferguson played Wayne Rooney in central midfield with Van Persie and Javier Hernandez forming a front two and the England man was hugely impressive.
The United manager said: "He was brilliant. I was thinking he possibly needed a different role in terms of getting his confidence back. He has been under a bit of criticism, not serious, but there were some doubters nonetheless.
"He's a fantastic player and our job is to get that confidence and form back. I thought a spell in midfield would do him the world of good and it worked for us."