Keane’s second multigoal game of the season helped the Galaxy (7-10-2) snap a two-match losing streak, and extended the Fire’s winless streak to two games (0-1-1).
Keane scored on a penalty kick in the 24th minute after Chicago defender Jalil Anibaba blocked a pass with his right hand at the edge of the penalty area.
Keane celebrated the second score with a pair of somersaults.
The Fire (8-6-4) managed only three shots, all in the second half, as Galaxy goalkeeper Josh Saunders collected his third shutout of the season. Saunders made his best save on Chris Rolfe’s low shot about a minute before Keane’s last goal.
Los Angeles star David Beckham served a one-game suspension, imposed by the league office for kicking two balls at San Jose’s Sam Cronin and subsequent involvement in a postgame scuffle with Cronin and other San Jose players on June 30. He also missed the Galaxy’s match with Philadelphia on Wednesday because of the yellow cards awarded on the play.
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