India started well and took the lead in the third minute through Shivendra Singh's deflection off a Tushar Khandker cross on counter attack.
Within two minutes, Indian goalkeeper and captain Bharat Chetri pulled off a two-stage save, sweeping the ball off the goal-line after having initially parried Rob Moore's reverse hit.
But James Tindall scored the equaliser through a 17th minute penalty corner and the teams were locked 1-1 at the half-time.
In the opening minutes of the second half, Britain goalkeeper James Fair brought off a smart save on the near post off a Khandker's attempt to score.
Ashley Jackson put his team ahead in the 45th minute off a penalty stroke. Harry Martin made it 3-1 with a 62nd minute goal off a deflection from Chetri when Jackson scooped the ball.
The next match in the tournament will feature Great Britain and Spain on Monday. India will play their next match against Spain on July 18.