The former Arsenal captain opened his account for his new club with a deftly guided volley to steer Patrice Evra's cross past Mark Schwarzer and into the far corner as United ran out 3-2 winners over Fulham.
The Netherlands striker's effort garnered a huge 42 per cent of the votes cast by Eurosport-Yahoo! readers.
In second place was Luis Suarez's low free-kick bent around the Manchester City wall as Liverpool held champions Manchester City to a 2-2 draw at Anfield.
And close behind in third was Fernando Torres's brilliant finish into the top corner with the outside of his foot after a clever backheeled return pass from new Chelsea star Eden Hazard.
Poll results - who scored the best Premier League goal of last weekend?
1. Robin van Persie (Man United v Fulham) 42%
2. Luis Suarez (Liverpool v Man City) 26%
3. Fernando Torres (Chelsea v Newcastle) 24%
4. Steven Pienaar (Aston Villa v Everton) 7%
5. Simeon Jackson (Norwich v QPR) 1%
(8313 votes cast as of 12:00 Friday August 31)