They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
Put into bat under a grey sky, India got off to a strong start with Lokesh Rahul, replacing injured Shikhar Dhawan at the top, and Rohit forging a 136-run stand for the opening wicket.
Rohit made 140 off 113 balls and raised 98 runs with Kohli but Mohammad Amir's tight bowling at the death overs denied India a 350-plus total.
Amir was the pick of the Pakistan bowlers claiming 3-47.