Dravid, who was bowled by the fiery Shoaib Akhtar one run short of his ninth Limited Overs century, led a spectacular batting spree by the Indians on a run-laden wicket at the National stadium in Karachi on Saturday.
India surpassed their previous best against Pakistan of 316 for seven at Dhaka in 1998 and left the hosts facing a stiff target of seven runs an over for an early lead in the five-match series.
India, on their first full tour of Pakistan since 1989, will also play three Test matches after the Limited Overs series ends on March 24.
Sehwag greeted Pakistan captain Inzamam-ul Haq's decision to field first by giving his team a flying start.
The free-stroking Delhi batsman, who smashed 14 boundaries and a six, put on 69 for the first wicket with Sachin Tendulkar and 73 for the second with skipper Sourav Ganguly.
Dravid and young Mohammad Kaif (46) built on Sehwag's blitzkreig by adding 118 for the fifth wicket to lift India past the 300-mark.
The match, played before a capacity crowd of 33,000 at the heavily guarded stadium, began dramatically when Akhtar conceded 10 runs in the opening over, including two wides and as many no-balls.
Akhtar was not the only player affected by nerves. Off the last ball of the over, Shoaib Malik spilled a simple catch in the covers off Sehwag.
In his second over, Akhtar forced Tendulkar to give a catch at square-leg -- only to see Australian umpire Simon Taufel declare a no-ball.
Tendulkar rubbed salt in the bowler's wounds by top-edging the last ball of that over to fine-leg for six, but fell to Akhtar soon after for 28 when he edged a catch to gully.
Rana Naveedul Hassan, who replaced Akhtar, was hammered for 24 runs in his first over and finished with 3-73 from 10 overs.
Sehwag and Ganguly took the total to 142 for one in the 15th over when Pakistan earned a lucky break.
Sehwag went on the backfoot to cut a slow ball from Hassan, missed the line and was bowled.
The run-rate slumped after Sehwag's dismissal as Pakistan hit back with the wickets of Ganguly and Yuvraj Singh in the space of six runs to make it 220 for four in the 29th.
But Dravid and Kaif joined hands to ensure the good start was not wasted.
Pakistan added to their woes by sending down 20 no-balls and 10 wides, giving India five extra overs to bat.