Put into bat, India lost a couple of early wickets after opener Shikhar Dhawan (11) and Virat Kohli (0) were scalped by Chris Woakes (4-52) with India reeling on 19 for two.
But Rohit Sharma (52) and Ajinkya Rahane (41) batted sensibly to lay a solid foundation for the middle-order to build upon.
Raina, registering his fourth ODI ton, then came good in the batting powerplays with Mahendra Singh Dhoni (52 off 51 balls) as his able partner put on a 144-run fifth-wicket partnership to propel India to a challenging score.
The Men in Blue managed 62 runs in the batting powerplays (35-40 overs) without losing a wicket as Raina raced to his fifty in 49 balls.
Raina's knock was laced with 12 fours and 3 sixes but finally the aggressive left-hander fell to Woakes in the 47th over.
Dhoni, hitting 6 boundaries, took over from Raina to register his 55th half-century of his ODI career but was finally cleaned up by Woakes.
In the end Ravichandran Ashwin (10 not out) and Ravindra Jadeja (9 not out) managed 13 runs in the final over to help India cross the 300-run mark.
Earlier in the innings, Rohit and Rahane also stitched a useful 91-run third-wicket partnership only to be sent back by England off-spinner James Tredwell (2-42).
England pace spearhead James Anderson (0-57), Chris Jordan (0-73), Ben Stokes (0-54) and Joe Root (0-14) went wicketless in the innings.
In the highlight of the innings, Raina and Dhoni batted together for 16.5 overs, putting on an entertaining display of attacking batting, scoring at 8.55 runs per over. Thanks to their stand, India scored 147 runs in the last 15 overs.
This was after rain had stayed away and England had won the toss, opting to field first. Alex Hales was handed his ODI debut while India opted for Mohit Sharma instead of Umesh Yadav and more importantly, Raina ahead of Ambati Rayudu.
Rohit and Dhawan walked out to open the innings. Under some cloud cover, they took their time at the crease as Anderson and Woakes swung the ball nicely. The monotony was broken by a nicely leant-in boundary by Rohit in the 3rd over.
But his running between the wickets with Dhawan left much to be desired given that these two batsmen have been opening the innings for some time now. It didn't result in a run-out miraculously though Dhawan didn't benefit from it, caught behind off Woakes.
It brought Kohli to the crease and he left three balls later for duck, out caught at mid-off thanks to an eager stroke to get off the mark.
At 19/2 in the 8th over then, it looked all too familiar for India, but Rahane and Rohit counter-attacked. They were watchful early on, knowing the importance of their stand, but opened up later to help along the run-rate.
India's first 50-run mark came up as late as the 14th over, but with Rohit-Rahane at the crease, they moved along just fine.
The duo brought up their 50-run partnership in the 16th over and ultimately put on 91 runs in batting 16.1 overs together, when Tredwell came in to wreck India's middle order.
After India's 100-run mark had come up in the 22nd over, the off-break bowler first had Rahane stumped in the 24th over, the batsman playing lazily off the crease.
Then, after he had reached his 23rd ODI fifty off 82 balls, Rohit threw it all away as he holed out to Woakes at long off trying to hit Tredwell out of the park in the 30th over.
Moving on, Raina and Dhoni made it work but the UP southpaw was lucky to escape a close LBW shout off Tredwell in the 32nd over when umpire Paul Reiffel turned his appeal down -- Raina was 17 then.
But after that everything seemed to work in India's favour and nothing went right for the hosts. An 11-ball over, consisting of 5 wides, from Woakes was a sign of a helpless England bowling attack for once.