Inspired by a century from man-of-the-match Virat Kohli, India piled up 300 for seven wickets in its 50 overs, with Pakistan dismissed for 224 in 47 overs.
The match was played before a sell-out crowd of over 40,000 at the Adelaide Oval, the vast majority supporters of the two powerhouses of Asian cricket.
Pakistan's pursuit of a formidable total on a slow wicket was hampered by indifferent batting against a persistent Indian bowling attack, led by paceman Mohammed Shami, who took four wickets for 35 runs.
Misbah-ul-Haq top-scored for Pakistan with 76 before giving Shami his fourth wicket, but he could find little support from its middle and lower order batsman and the result had an air of inevitably about it as wickets tumbled.
Earlier, Kohli, given two chances when dropped on three and 76, became the first Indian player to score a century against Pakistan in a World Cup match.
He shared century stands with opener Shikhar Dhawan (73) and Suresh Raina, who smashed 74 off 56 balls against a wilting Pakistan bowling attack, with 83 runs coming off the final 10 overs.
Sohail Khan led the Pakistan attack with five wickets for 55 runs, but was expensive in his closing overs.
"It's one of the biggest wins of my career. It's amazing to start like this," said Kohli, who was scoring his 22nd one-day international century.
"Expectations of me will rise but I just look to stand up to it.
"I hate losing. I love to win and play for my country. My role is to play a long innings so that the power hitters can play with freedom," he added.
Pakistan captain Misbah acknowledged his team had lost to the better side on the day.
"They played well, posted a good total and bowled well. When we lost wickets in the middle it made it hard," he said.
The opening weekend of the six-week long tournament has seen victories for joint hosts Australia and New Zealand against England and Sri Lanka respectively, while earlier Sunday South Africa beat Zimbabwe by 62 runs.
The 14 teams in the World Cup, which is held over four years, are divided into two pools of seven teams each with the top four from each group qualifying for the quarterfinal knockout stage.