India reached 166/8 in response to England's 165/9, extending their series lead to 2-0.
The Indian batting lineup struggled against pace bowling. Mark Wood dismissed Abhishek Sharma for 12, whilse Jofra Archer removed Sanju Samson during a pull shot attempt.
Captain Suryakumar Yadav managed three boundaries before Brydon Carse bowled him in the sixth over. Carse struck again two overs later, having Jurel caught for 4 to make it 66/4. The situation worsened to 78/5 when Jamie Overton dismissed Hardik Pandya for 7.
Varma maintained India's hopes through a 38-run stand with Washington Sundar, who became Carse's third victim in the 14th over.
However, Varma held his nerve and mixed caution with aggression to take India to victory, while receiving valuable support from number 10 Ravi Bishnoi, who contributed 9 not out, including two boundaries from 14 deliveries.