Raina smashed a superb century off just 75 deliveries to anchor India’s innings of 304-6 on a dull day in the Welsh capital, before left-arm spinner Jadeja's figures of 4-28 led the tourists' attack to dismissing England for 161 off 38.1 overs in reply.
India's 133-run Duckworth-Lewis victory - England's reply was limited to 47 overs following a slight rain delay - puts them 1-0 to the good with three ODIs remaining after Monday’s opener in Bristol was abandoned.
England skipper Alastair Cook elected to field after winning the toss, and that looked to be a good decision when James Tredwell (2-42) and Chris Woakes (4-52) struck early to leave India 19-2.
Shikhar Dhawan (11) and Virat Kohli (0) were the men to fall, with the latter’s horror show of a tour - he scored just 154 across the five Tests - continuing.
Ajinkya Rahane (41) and Rohit Sharma (52) settled the ship before Jos Buttler stumped the former off the bowling of Tredwell in the 24th over.
Tredwell then removed Rohit soon after as he miscued an attempted drive straight to Woakes at long-off to leave India 132-4.
Enter man of the match Raina.
The 27-year-old began in measured fashion - scoring 43 off 47 balls - before then cutting loose to rack up a quickfire century that included 12 fours and three sixes.
Partnered excellently by captain MS Dhoni (52 off 51 balls), Raina took the game away from England before being caught at the boundary by an off-colour James Anderson (0-57) when trying to slog Woakes.
Pace bowler Chris Jordan did England no favours, posting figures of 0-73 - including 12 wides.
Set a target of 295 from 47 overs after a brief shower, England began their reply in solid if unspectacular fashion, with captain Cook (19) and debutant Alex Hales (40) opening.
Mohammed Shami (2-32) struck twice in the 11th over to remove Cook and Ian Bell (1), though, and England wobbled further when Joe Root was dismissed by Bhuvneshwar Kumar (1-30) for just four soon after.
Hales attempted to force the issue and became Jadeja’s first victim of the day in the 21st over, and Buttler (two) and Eoin Morgan’s (28) dismissals left England in trouble at 119-6.
Jadeja quickly removed Ben Stokes (23) and Jordan’s bad day at the office continued when Raina (1-12) trapped him lbw for a duck.
Woakes (20), Tredwell (10) and Anderson (nine not out) offered futile resistance, but India claimed an easy win that exacts a measure of revenge after England won the last three Tests of the series at a canter.