Van Persie took a cross from Antonio Valencia on his chest at the back post and dispatched a fine left-foot volley past Kelvin Davis.
The Netherlands striker's effort garnered 38 per cent of the votes cast by Eurosport-Yahoo! readers and gave him the award for the second week running.
In second place was Hatem Ben Arfa's thunderous effort in Newcastle United's 1-1 draw with Aston Villa.
Third place went to Lukas Podolski for his neat one-two with Santi Cazorla for Arsenal against Liverpool.
Poll results - who scored the best Premier League goal of last weekend?
1. Robin van Persie (Manchester United v Southampton)
2. Hatem Ben Arfa (Newcastle v Aston Villa)
3. Lukas Podolski (Arsenal v Liverpool)
4. Moussa Dembele (Tottenham v Norwich)
5. Wayne Routledge (Swansea v Sunderland)