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.
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.
It meant they matched Ireland’s unbeaten start to the tournament after two rounds of action, but Italy now look set for a potential wooden-spoon clash at home to Scotland later this month.
“We did some good work for 55-60 minutes,” Saint-Andre said.
“We scored three tries, but nothing happened in the last 20 minutes.”
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.
Asked about the sendings-off, Saint-Andre said he needed to look at video footage, but Slimani and Rizzo will now face disciplinary hearings.
It meant France were briefly reduced to 13 players following the sin-binning of lock Sebastien Vahaamahina for kicking the ball away.
France scorers: Tries: Picamoles, Fofana, Bonneval. Cons: Doussain 3. Pens: Doussain 3.
FRANCE: Dulin, Huget, Bastareaud, Fofana, Bonneval, Plisson, Doussain, Domingo, Szarzewski, Mas, Pape, Maestri, Nyanga, Le Roux, Picamoles.
Replacements: Fickou for Bastareaud (70), Trinh-Duc for Plisson (66), Machenaud for Doussain (60), Forestier for Domingo (48), Kayser for Szarzewski (57), Slimani for Mas (48), Vahaamahina for Pape (66), Chouly for Picamoles (57).
Italy scorers: Tries: Iannone. Cons: Orquera. Pens: Allan.
ITALY: McLean, Iannone, Campagnaro, Garcia, Sarto, Allan, Gori, De Marchi, Ghiraldini, Castrogiovanni, Geldenhuys, Furno, Minto, M. Bergamasco, Parisse.
Replacements: Orquera for Allan (63), Botes for Gori (63), Rizzo for De Marchi (58), Giazzon for Ghiraldini (58), Cittadini for Castrogiovanni (58), Bortolami for Geldenhuys (70), Zanni for Minto (51).
Referee: Jaco Peyper (South Africa).