Defeat was a blow for three-time Olympic Games silver medallists Lithuania, but is unlikely to deny them a place in the knockout stage.
It looked at one point, though, as if the Baltic side's progression might be a whole lot easier as they turned a nine-point deficit in the first quarter into a 43-39 lead by half-time, helped by two quick-fire three-pointers from Martynas Pocius.
But Parker, wearing distinctive goggles to protect an eye injury, inspired his side to a recovery, finishing with nine field goals, including two three-pointers, and seven free throws.
The third quarter was key, France winning it 20-9, as their opponents' accuracy from outside the circle deserted them.
Nicolas Batum followed Parker with 21 points and Ronny Turiaf led the way on the rebound count with 10.
Pocius was Lithuania's top scorer with 18, while captain Linas Kleiza had 17.
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