Errani faces Maria Sharapova on Saturday in the singles final and is bidding to become the first woman since Mary Pierce in 2000 to win both championships at the French Open.
"Today is a special day for us and for sure tomorrow is a special day for Sara," Vinci said on court.
They hugged at the end of the match, both kissing the Simone Mathieu Cup.
"I think playing doubles also (makes) me better physically," Errani said.
She and Vinci were the doubles runners-up at the Australian Open in January. They are unbeaten on clay this season, winning 23 matches and titles in Acapulco, Barcelona, Madrid and Rome.
On Friday, they dropped the first set on a backhand volley winner from Kirilenko.
Errani hit a forehand winner to break for a 5-4 lead in the second and a backhand volley from Vinci evened the match at one set apiece.
The Italians broke serve three times in the final set, clinching victory when Petrova hit a forehand return long.
Errani is the first player since Kim Clijsters in 2003 to reach the finals of singles and doubles at Roland Garros.
"She's strong," Vinci said. "She has nothing to lose tomorrow."