The 34-year-old, who returned to his first club in January after 14 years away, came on for Jens Toornstra to make his fourth appearance and scored under a minute later.
In a congested penalty box, former Watford winger Steven Berghuis flicked the ball into Van Persie's path before the Netherlands international neatly tapped the ball around Yoel van Nieff and curled his shot into the bottom corner.
Winding back the glory days.
Thursday night's 3-0 victory moves Feyenoord up to fourth in the Eredivisie table, but are 19 points behind leaders PSV.
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