Juan Carlos Navarro added 12 points and Pau Gasol 10 for the Spanish, the 2008 silver medalists who advance to play Russia on Friday.
Trailing 57-54 after Nicolas Batum's basket with 6:51 to play, Spain didn't allow another point until Mickael Gelabale's meaningless jumper with 5.5 seconds remaining, ending a two-game losing streak.
Tony Parker and Boris Diaw each scored 15 points for France, which grew frustrated at the finish and committed two unsportsmanlike fouls in the final half-minute.
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