Raina scored 100 off 75 balls and Rohit Sharma and MS Dhoni also hit half-centuries as the tourists posted 304-6.
Ravindra Jadeja then claimed four wickets as England subsided to 161 in their rain-adjusted chase of 295.
Alex Hales hit 40 on his debut but England will have to come from behind in the five-match ODI series.
The hosts began promisingly enough after Alastair Cook won the toss and elected to bowl under grey skies.
Chris Woakes was an impressive performer in Birmingham’s Twenty 20 Finals Day victory at the weekend and the seamer continued his good limited-overs form as he removed two of India’s most out-of-form batsman in an early burst.
First Shikhar Dhawan edged behind to Jos Buttler attempting an extravagant drive, then Virat Kohli inexplicably drilled his second ball straight to Cook at mid-off.
At 19-2 after eight overs, India were in trouble, but Sharma and Ajinkya Rahane showed the sort of application India lacked so badly in the Test series as they rebuilt the innings.
Rahane fell to the excellent James Tredwell for 41, but the breakthrough failed to check India’s momentum as it brought Raina to the crease.
The left-hander looked fluent from the start, timing the ball sweetly as he combined with first Sharma and then Dhoni to accelerate the Indian innings.
England gave the tourists plenty of assistance with a wayward bowling performance, with Chris Jordan particularly culpable as he sent down 12 wides in returning figures of 0-73 from his 10 overs, including five in one 11-ball over.
India plundered 133 runs off the last 13 overs, with Raina reaching his fourth ODI century off 75 balls as India posted 304-6.
A brief rain delay after the interval ensured that England would chase an adjusted target of 295 off 47 overs, and when the showers abated, the hosts began brightly enough.
Cook and debutant Hales compiled 53 off the first 10 overs before Mohammed Shami swung the match decisively in India’s direction.
The paceman removed Cook and Ian Bell within three balls, and when Joe Root perished to Bhuvneshwar Kumar soon after, England were 63-3.
Hales played some stylish shots on his debut but he was caught for 40 trying to sweep Jadeja, before the spinner removed Buttler for two.
England’s last hopes rested with Eoin Morgan, but when the Middlesex batsman fell to Ravichandran Ashwin for 28, the game was up.
Jadeja claimed two tail-end wickets to finish with impressive figures of 4-28 as India completed a straightforward victory.
The crushing win provides a much-needed fillip for the tourists, who werecomprehensively beaten 3-1 in the Test series.
England meanwhile have now lost four of their last five ODIs, and their search for a consistent winning formula in the 50-over format continues with the World Cup just six months away.