Leedham once again shone for Britain with a game-high 16 points as they matched their experienced Group F rivals until the final quarter before a late 12-2 run saw off their challenge.
The win secured Belarus their place in the quarter-finals as well as the Czech Republic, who beat Britain 66-55 on Wednesday, with hosts France sitting top of Group F.
Britain and Serbia are left to battle it out for the final quarter-final place with the former to play Croatia, who cannot qualify, next and the latter to face the Czech Republic.
And Leedham said: "It's a tough loss for us. We didn't play solidly enough. They just out-hustled us and won the possession game and worked harder than us.
"When we're not getting those hustle plays, that minimises our chances of winning because we're a blue collar team. We've got one more game on Sunday and we really have to show our brand of basketball."