Kohli made 107 and shared century stands with both Shikhar Dhawan (73) and Suresh Raina (74) at the Adelaide Oval.
When Kohli fell as part of Sohail Khan's 5-55, Pakistan looked to have dragged themselves back into the game by restricting India to a reachable 300-7.
But a chase that never gained momentum was wrecked by a collapse of three wickets for one run and they eventually stumbled to 224 all out, Mohammed Shami claiming 4-35.
In isolation, India's win earns national pride in what was billed as the most watched cricket match of all time, with an estimated television audience of one billion, and extends their World Cup record against Pakistan to six wins from as many matches.
It was also an emphatic way to begin the defence of a trophy they won on home soil in 2011 and represents their first competitive win since arriving for a tour of Australia in November.
Pakistan, winners when the tournament was last held in Australia and New Zealand 23 years ago, can take heart from the way they stuck to the task with the ball, but their limp chase was poor. (BBC)