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.
The Dutchman 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."
Stoke, meanwhile, are dropping like a stone towards the relegation zone and find themselves 16th following Sunderland's win over Newcastle. Wigan in 18th are only three points behind the Potters but have two games in hand and Stoke's next three games against QPR, Norwich and Sunderland will go a long way to determining their fate.
Manager Tony Pulis still believes two wins from their final five games will see Stoke stay up, with their goal difference better than many of the teams around them.
The Welshman said: "I've just spoken to the players. It's a five-game season.
"There's eight, maybe nine teams that are in the scrap and we've just got to make sure, no matter what's happened before, the season really starts for us now. I still say 40 points will do it."
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