Number eight Louis Picamoles, centre Wesley Fofana and debutant wing Hugo Bonneval all crossed during a devastating nine-minute spell early in the second period as France triumphed.
But the closing stages will be remembered for red cards rather than running rugby as South African Jaco Peyper sent off substitute props Michele Rizzo and Rabah Slimani.
Italy forward Rizzo started the skirmish with a head-butt, and when Slimani reacted in similar fashion Peyper brandished red cards after conferring with his assistant Craig Joubert and consulting television replays.
They became the first players to be sent off in a Six Nations game since 2006 when Scotland lock Scott Murray was dismissed against Wales in Cardiff.
Scrum-half Jean-Marc Doussain kicked three conversions and three penalties to underline French dominance, while Italy replied with a late Tommaso Ianonne try, converted by Luciano Orquera, and fly-half Tommaso Allan slotted a penalty.
France coach Philippe Saint-Andre made three changes from the side that inflicted an agonising defeat on England last weekend, with Bonneval, hooker Dimitri Szarzewski and lock Yoann Maestri all called up.
Italy, meanwhile, with just one win from 37 previous Six Nations away games, showed five switches after a 23-15 loss to Wales last time out, including experienced forwards Marco Bortolami and Alessandro Zanni being dropped to the bench.
Despite going into the contest as underdogs, Italy kept France scoreless during an error-strewn opening quarter notable only for a high penalty count on both sides, with Doussain and centre Gonzalo Garcia each missing two shots at goal.
It took France 27 minutes to break the deadlock when Doussain finally found his range, but Allan quickly cancelled that out before he missed an easy chance as Italy established some momentum through the powerful running of prop Alberto Di Marchi.
Doussain, though, kicked two further penalties before the break, giving France a 9-3 interval advantage and setting them up for a strong second-half showing.
And Les Bleus did not disappoint, stunning Italy with two converted tries in as many minutes just after the restart.
Picamoles powered over for the first from 15 metres, with Doussain adding the extras, then before Italy had time to regroup they were undone by Fofana's brilliance.
The Clermont Auvergne star broke two tackles on a surging run to the line for his ninth try in 23 Tests, and Doussain's conversion meant France were 20 points clear and well on the way to an emphatic triumph.
France had put their foot to the metal, and Italy had no answer, although they contributed to Les Bleus' third try when Fofana intercepted a pass just inside his own half that showcased stunning back play.
Yoann Huget appeared on Fofana's left shoulder and sprinted deep into Italy's 22, and when he was hauled down, Bonneval gathered to finish off a sweeping move.
Doussain's conversion made it 30-3, with Italy reeling from conceding three tries in rapid succession and having no way back into the contest.
Tempers frayed during the closing minutes, and after replacement French lock Sebastien Vahaamahina was sin-binned for kicking the ball away, Peyper opted to send off Slimani and Rizzo following a dust-up between the packs.
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