Bolton took advantage of a defensive error from Gerard Pique to score. When Pique tried to head clear a free kick from Ivan Campo, he missed completely, and Anelka took the loose ball and scored in the 11th minute.
Carlos Tevez beavered away without much success, as did Louis Saha, while wide pair Ryan Giggs and Nani were virtually anonymous.
To make matters worse for United, Sir Alex Ferguson was sent to the stands by referee Mark Clattenburg for a half-time tunnel rant at a succession of minor decisions that had gone against his team.
Bolton: Jaaskelainen, Hunt, Meite, Andrew O'Brien, Gardner,Campo, Nolan (McCann 83), Guthrie (Wilhelmsson 74),Davies (Speed 70), Anelka, Diouf.
Subs Not Used: Al Habsi, Michalik.
Man Utd: Van der Sar, Brown (O'Shea 88), Pique (Anderson 59),Ferdinand, Evra, Nani, Carrick, Hargreaves, Giggs, Saha, Tevez.
Subs Not Used: Kuszczak, Fletcher, Eagles.
Goals: Anelka 11.
Referee: Mark Clattenburg (Tyne & Wear).
Booked: Davies, Nolan, Hunt (Bolton)