Seeded seventh in the tournament, Sania and Vesnina beat their fourth seeded opponents 6-3, 2-6, 6-4 in 105 minute semifinal contest at the Roland Garros.
In the final, the Indo-Russian combo will face the unseeded Czech duo of Andrea Hlavackova and Lucie Hradecka who beat third seeded pair of Vania King of United States and Yaroslava Shvedova of Kazakhstan 6-3, 6-3 in another semifinal.
This is Sania's third Grand Slam final appearance in her career -- the first two being in the mixed doubles in the Australian Open.
Sania and ace compatriot Mahesh Bhupathi had won the Australian Open mixed doubles in 2009 while they were the losing finalists in the same Grand Slam tournament in 2008.
Sania, who paired up with Vesnina only in February, had a strap around just below her left knee but did not show any apparent problem as she played some superb winning shots across the net.
Sania and Vesnina broke their opponents early in the first set to race to 4-1 ahead before pocketing it 6-3 in 30 minutes.
The second set was a longer affair with both sides breaking serves though Sania and Vesnina were broken thrice in their serves to lose it 2-6 in 38 minutes. In the deciding set, Sania and Vesnina broke their opponents' serve in the first game itself and held theirs to take a 2-0 lead.
Huber and Raymond held onto their next serve but Sania and Vesnina maintained their two-point lead at 3-1 by winning the fourth game. But in the sixth game, Sania and Vesnina were broken and the score was levelled 3-3.
The Indo-Russian pair responded in a superb fashion by breaking their opponents in the seventh game to surge ahead 4-3 before holding serve to make it 5-3.
Huber and Raymond held their serve in the ninth game to make it 4-5. But Sania and Vesnina held onto their nerves to ensure that they did not blow away their serve to take the third set 6-4 in 37 minutes and reach their first Grand Slam final together.
Since their first pairing in February, Sania and Vesnina had won two titles -- at Indian Wells in March and in Charleston in April.