Nick Cassidy (28) was second for Envision Racing with Porsche's Antonio Felix da Costa (31) promoted to third in his 100th race after Envision's Sebastien Buemi (34) was handed a 17 second post-race penalty for an overpower infringement.
The win was Vergne's 11th in Formula E but first in two years and the double champion needed an energy-saving defensive drive to hold off New Zealander Cassidy in the closing laps near the Hussain Sagar lake.
Cassidy had twice as much energy remaining as the Frenchman but could not get past, the cars finishing nose to tail and separated by 0.4 seconds.
"I like new tracks... especially this one is a lot of fun," said Vergne.
"I guess when there are still a lot of little secrets to find on the track, I probably find them quickly enough."
New Zealander Mitch Evans (28) started on pole position, with Vergne second, but was shunted out by Jaguar teammate Sam Bird (36) on lap 13 with both retiring.
NEOM McLaren's Jake Hughes (28) retired after spearing into the wall and telling his team over the radio that "the mirror got stuck behind the steering wheel".
The fourth round of the 16-race electric championship was the first time in 10 years that a top-tier FIA-sanctioned series had visited India.
Vergne was there last time too, competing for Red Bull-owned Toro Rosso in the 2013 Indian Formula One Grand Prix at the Buddh circuit near New Delhi.
Wehrlein, winner of two of the first three races, now has an 18-point lead over Porsche-powered Avalanche Andretti rival Jake Dennis.
Formula E's next race is another first, this time in Cape Town for South Africa's series debut on February 25.
