Dravid, who sent England in to bat, saw the home team pile up 288 for two with man-of-the-match Ian Bell (126 not out) and opener Alastair Cook (102) both scoring their maiden one-day international hundreds.
India, in reply, slumped to 34 for four inside 12 overs under the floodlights with pace bowler James Anderson striking three times on his way to career-best figures of four for 23.
They were bowled out for 184 off the last ball of the match after Dravid had top scored for his team with 46.
Andrew Flintoff, in his first England appearance since the World Cup following a third operation on his left ankle, took a miserly one for 12 in seven overs after Lancashire team-mate Anderson's initial burst.
"I thought there would be a bit more for the bowlers in the wicket," said Dravid, defending his decision to field first.
"The partnership between Bell and Cook (178) was a good one. They really put us under pressure."
India struggled to take wickets on a good pitch and Dravid admitted finding the right balance in his bowling attack was a problem. "For us, it's a bit of an issue because of the lack of a genuine all-rounder."
Earlier this month India wrapped up a 1-0 Test series win at The Oval and Dravid, asked after Tuesday's game if there had been an emotional let-down replied: "Maybe a little bit, but that's not an excuse. Credit to the opposition. They played a perfect one-day game.
"They really batted well, got two guys who went on and got a hundred. It's exactly what you want. They then took wickets up front with the new ball."
India didn't help themselves with some sloppy outfielding and careless running between the wickets.
"It's an area we've got to try to improve," Dravid said. "On big grounds like this, we are not overnight going to get strong arms and big throws.
"Not making stupid mistakes running between the wickets, that's something we can definitely control and work on."
"It's been a disappointing performance all round but there are six games to go and hopefully we'll bounce back."
England captain Paul Collingwood, who earlier this season saw his team go 1-0 up in a one-day series against the West Indies before losing 2-1, cautioned against getting carried away.
"I don't want to sound too downbeat but it's one good performance and we have to make sure we have another six.
Bell's hundred was his first at this level in 48 one-day internationals.
"I guess it is a bit of relief," said the 25-year-old Warwickshire batsman. It's taken time. It's nice that me and Cookie could get hundreds on the same day but to be there at the end was satisfying.
"The key for me, and where I've made mistakes in the past, was my shot selection. That was much better."
England's win came with the added bonus of seeing Flintoff bowling at in excess of 92 mph.
"Fred (Flintoff) was fantastic," said Collingwood. "He was raring to go. He's a world-class player and I'm glad to have someone like that back.
"The areas Freddie bowls in it's very hard to score, especially at that kind of pace."
However, Collingwood stressed: "Consistency is the crucial thing. Today (Tuesday) was a kind of a perfect game but we need to do that again and again."
The series continues on Friday, with another day/night match, at Bristol.