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.
Pocius was Lithuania's top scorer with 18, while captain Linas Kleiza had 17.