The Netherlands striker grabbed his ninth league goal when his shot deflected off James Collins and over the head of goalkeeper Jussi Jaaskelainen after just 32 seconds, making it the quickest goal in the league this campaign.
With United lacking any real fluency, Carlton Cole came close to snatching a draw for the mid-table visitors but his close-range attempt was blocked by goalkeeper Anders Lindegaard.
United\'s fourth straight home win kept City at arm\'s length after the champions\' 2-0 victory at Wigan on Wednesday, and saw Van Persie get back in the goals after three scoreless games. He now has 12 goals in 18 matches in all competitions this season after his move from Arsenal in August.
\"Robin van Persie is a quality player and we have largely kept him quiet,\'\' West Ham manager Sam Allardyce said. \"But he will score 20 goals for Manchester United, maybe 30, (this campaign).\'\'
His effort had more than a hint of good fortune in it, flicking a pass from Michael Carrick over marker Winston Reid before seeing his attempted lob loop off Collins into the net.
United failed to kick on, though, and was kept largely quiet by a compact West Ham side.
\"We got a great start,\'\' United manager Alex Ferguson said. \"You hope to go on from a start like that and some of our football was very good, but we never quite finished them off.\'\'
With Wayne Rooney struggling to make an impact as an attacking midfielder, West Ham tried to respond through shots by Kevin Nolan and Andy Carroll that both flew off target.
United ended up hanging on for a scrappy victory, with the team yet to click this season.
\"Of course, City are on our tails so it is going to be a long season,\'\' Ferguson said.
The first Manchester derby takes place at City\'s Etihad Stadium on Dec. 9.