Left-handed Jamshed smashed a 104-ball 112 for his maiden one-day century and Hafeez a 113-ball 105 for his fourth hundred to boost their team's hopes of posting a third successive win.
The pair put their team on course for a big total with a 224-run stand, Pakistan's best for the opening wicket against India in one-day internationals.
The day-night match is the first between the two teams since the high-profile World Cup semi-final at Mohali last March, which India won on their way to clinch the showpiece title.
Jamshed and Hafeez dominated the Indian attack, playing attractive shots during their 35.5-over stand to help their team maintain an impressive run-rate from the beginning.
Pakistan scored 73 in the last 10 overs, with Younis Khan hitting a 34-ball 52 with the help of six fours before falling to a superb one-handed catch by Suresh Raina in the covers off paceman Praveen Kumar.
Shahid Afridi (nine) completed 7,000 one-day runs before being caught by Virat Kohli off Irfan Pathan.
Hafeez was the first to complete his century, pushing Kumar to mid-off for a single. He struck one six and nine fours before being trapped leg-before by seamer Ashok Dinda.
Jamshed reached the century in Kumar's next over with a single and then hit the bowler for a six. He also cracked 10 fours.
India, who failed to defend 289 in their last match against Bangladesh on Friday, again put in a below-par performance as none of their bowlers could keep pressure on the Pakistani openers.
Skipper Mahendra Singh Dhoni used eight bowlers, including part-time spinner Sachin Tendulkar who bowled just 10 deliveries before he was injured attempting to hold a return catch off Jamshed when the batsman was on 69.