The French had the upper hand from the off, but the game swung decisively their way when Tongan scrum half Taniela Moa was sin-binned for an elbow on Dimitri Szarzewski.
At 14-6, Tonga were still in it, but Damien Chouly powered over in first half injury time to make the most of the man advantage.
Tempers then boiled over after the break when Tonga prop Sona Taumalolo and French lock Yoann Maestri were red carded after a flurry of punches were thrown.
Kalamafoni was prominent with a strong carry in the build up to Fetu'u Vainikolo's first try. The Exeter wing would add a second as time ran out, but 38-18 was a fine win for the French.
Meanwhile, in Cremona, Fiji paid the price for ill discipline as they saw five men sent to the sin bin, four in an eight minute period, in a bizarre encounter.
Qera was the first to go. He picked up an Italian runner and somehow managed to turn him upside down, However, he was in full control and lowering him to the ground when Martin Castrogiovanni landed an absolute haymaker on him.
Castrogiovanni, making his 100th international appearance, escaped punishment while Qera was sent to the sin bin, where he was soon joined by Tikoirotuma, Matadigo and Nasiganiyavi.
Italy made the most of it to open up a 20 points to 5 lead, but they never quite finished off a battling Fiji side who ran in some superb scores in the second half to narrow the gap to 37-31 and threaten an incedible comeback before time ran out.