England took an early lead after Steven Gerrard rounded off a fine move but Green, given the nod ahead of David James, committed a dreadful mistake that gifted the United States a draw.
He let a tame shot from Clint Dempsey slip through his grasp and into the net shortly before half-time.
Algeria, the Arab's only representative in the World Cup, meet Slovenia in the other Group C match on Sunday.
England, who enjoyed a fine qualifying campaign under Italian coach Fabio Capello, started brightly and managed to break the deadlock after six minutes.
A superb exchange of passes between striker Emile Heskey and Gerrard released the England skipper who steered a low shot past US keeper Tim Howard.
Capello was forced to substitute central defender Ledley King, who is suffering from fitness problems, with Liverpool's Jamie Carragher.
King, along with his partner John Terry, was capable of keeping US strikers at bay in the first half but Carragher hardly emulated his form after the interval.
Jozy Altidore almost gave the US a surprising victory when he out-muscled Carragher and raced clear but his shot was blocked by Green onto the post.
England still wasted some decent opportunities through Shaun-Wright Philips, Heskey and Wayne Rooney that could have given them a much-needed victory.