The Netherlands winger scored in the 77th minute after coming on as a substitute at Anfield as Liverpool rallied after allowing Carlos Tevez to score for United in just the third minute.
United defender Wes Brown scored a calamitous own-goal after a mix-up with goalkeeper Edwin van der Sar in the 27th, to the dismay of United manager Alex Ferguson.
"The two goals we lost were absolute shockers," Ferguson said. "The defending was very, very poor. People will think they are watching a (lower-division) side when they see the highlights."
It was manager Rafa Benitez's first league victory over Ferguson, with Liverpool's last Premier League win over United coming at Old Trafford in April 2004 just before his arrival. It was also Liverpool's first win over United at Anfield since January 2001.
Also Saturday, Emmanuel Adebayor scored three goals to lead Arsenal to a 4-0 win over Blackburn, and Chelsea overcame Robinho's debut goal to beat Manchester City 3-1 win.
Chelsea tops the standings with 10 points and leads Liverpool on goal difference. Arsenal is third on nine points, while City's loss was a reality check for a club about to become the richest in the world following the completion of a takeover by Arab investors - whose first move was to sign Brazil striker Robinho from Real Madrid for a British record transfer fee.
