The strike was the second goal of the Dutchman's brilliant first-half hat-trick in last month's 3-0 victory which also clinched a 20th league title for the Reds.
Van Persie, whose goal received 70% of the total votes, had put United ahead after just two minutes, before his sublime finish on 13 minutes.
Wayne Rooney collected the ball in his own half before floating a magnificent 40-yard pass into the path of van Persie whose first-time left-foot volley flew past Brad Guzan. On the goal, Robin said recently: "It was instinct. I looked up and thought: 'This ball is so nice, it's too beautiful to take a touch.' Had it been half a metre to the left or right I couldn't have hit it.
Wayne and I had been talking about playing balls in behind the right centre-back all week. We'd talked about it in training almost every day, then before the game Wayne said: 'Robin, don't forget that ball, I'll give you that ball today.' And it was the perfect pass, it was phenomenal. All I had to do was time my run correctly. In the last second I decided to hit it and I was lucky everything fitted together."
Robin beat off competition from Rafael and Wayne Rooney to win the Goal of the Season prize after polling 70% of the votes. Rafael's belter away at QPR was second with Wayne Rooney's long-range effort in the home win over Norwich finishing third.