Chasing 151 for a victory, Sharma (73 off 47) and Fazal (45 off 37) put on 87 runs for the opening stand to set the base for Vidarbha's win.
Apoorv Wankhade (17 not out) and Himanshu Joshi (14) too contributed to get Vidarbha over the line, reaching 154 for three in 18.3 overs.
Sharma, who feel just 16 runs short of the target, decorated his innings with nine boundaries and one six.
Earlier electing to bat, Tamil Nadu did not have the best of starts and were reduced to 59 for three inside nine overs.
But Baba Aparajith (41), captain Rajagopal Satish (32) and J Kousik (23) took the southern side to a respectable score.
Ravikumar Thakur (2/22) and Ravi Jangid (2/32) accounted for two Tamil Nadu wickets each.
Brief Scores:
Tamil Nadu: 150 for eight in 20 overs (Baba Aparajith 41; Ravikumar Thakur 2/22).
Vidarbha: Jitesh Sharma 73, Faiz Fazal 45; Rahiul Shah 2/31).
