Garbisi almost ran out of time to kick the penalty after the 80th minute and Italy just missed out on their second victory in France since a 40-32 win in Grenoble in 1997 after Les Bleus played the second half with 14 men following Jonathan Danty's red card.
The result left France's hopes of clinching the title in tatters after they could only score through Charles Ollivon's try and three penalties by Thomas Ramos.
Italy, without a win the Six Nations since 2022, scored a try by Ange Capuozzo, a Martin Page-Relo penalty and points from the boot of Garbisi.
"It's tough, really tough. We've had a lot of chances in the first half when we could have scored three or four tries," France centre Gael Fickou said.
"We will have regrets I think. We're still good friends," Italy and Stade Toulousain fullback Capuozzo said.
France, without mercurial scrumhalf Antoine Dupont - who has temporarily switched to Rugby Sevens for the Paris Olympics - and injured flyhalf Romain Ntamack, were rewarded for a blistering start with Ollivon try's and a penalty by Ramos.
They were all over Italy but missed a handful of clear try chances with handling errors and some poor choices, making simple things too complicated.
Flyhalf Matthieu Jalibert then left the pitch with a knee injury, prompting a major reshuffle with Thomas Ramos moving up to number 10 and Matthis Lebel, who was called up on Saturday after Louis Bielle-Biarrey pulled out injured, taking up the fullback role as Yoram Moefana came in on the wing.
Les Bleus reached halftime on a sour note as centre Danty was sin-binned for head-on-head contact with Juan Ignacio Brex and the yellow card was upgraded to a red.
A trade of penalties maintained a seven-point advantage for France but Italy came knocking with increased pressure.
With 10 minutes left, Capuozzo collected a pass from Leonardo Marin and dived over in the corner before Garbisi converted to level.
As France pushed for the win in the dying seconds, Italy were awarded a penalty after the clock had turned red but the ball fell from the tee and Garbisi was left with a handful of seconds to kick it.
The ball sailed low and crashed onto France's left post, leaving both teams with huge regrets.
"The ball falling (from the tee), I don't think it happens a lot," said Capuozzo.
