Kuznetsova looked set to be crowned champion after twice being runner-up at Indian Wells when she led 4-1 in the second set after taking the first, but Vesnina simply refused to be accept defeat.
The 14th seed, playing her first Premier Mandatory final, was rewarded for her remarkable resilience with a 6-7 (6-8) 7-5 6-4 in a showdown which lasted just over three hours in the California heat.
There were 16 service breaks in a gripping contest which swung one way and another before Vesnina finally came out on top, securing only her third WTA singles title - and a first since 2013 - to go 13th in the rankings.
Vesnina, a winner over world number one Angelique Kerber en route to the final, went 4-2 up in the first set courtesy of a fizzing backhand at the feet of the eighth seed, who netted.
But Kuznetsova broke straight back and had the set in the bag when her shot hit the net cord and dropped over the other side as a big stroke of luck helped her win the tie-break.
The 31-year-old breezed into a 4-1 advantage in the second, but Vesnina was not finished yet and reeled off four games in a row to go in front, also hitting back after failing to serve out the set as she broke yet again to take the match to a decider.
Both players showed incredible staying power with the sun beating down and Kuznetsova, playing her 40th final on the WTA tour, was just two games away from finally putting Vesnina away at 4-2.
But yet again back came Vesnina, who dropped to the floor after her compatriot sent a backhand just beyond the baseline to lose in the final for a third time.