Gaia Gorini scored 13 points for Italy while Mélanie Devaux led France with 12.
Neither team made much progress in the first quarter, trading the lead and ending the quarter in a 14-14 stalemate.
France went scoreless for almost five minutes in the second quarter until Sabrine Bouzenna made a basket from the low post and initiated a 5-0 run that tied the score at 19-19. However, Italy's team effort at the end of first half pushed ahead 30-26 before the break.
Devaux shined for France with excellent long range shooting and it was she who hit a come-from-behind trey to put her team ahead 42-39 at the end of the third quarter.
The roller-coaster basketball continued in the fourth quarter until Beatrice Carta had a chance to secure victory for Italy in the end with the score tied at 54-54, but she missed both free throws and sent the game to overtime.
Neither team was ready to give up in the extra period until Francesca Dotto went to the foul line with 0:30 to go and hit a pair of free throws that gave the Italians a dramatic victory and first palce in their Qualifying Round group.