Left-hander Chanderpaul, batting at No 3, made 116 not out in a total of 278 for five after West Indies, who levelled the three-match series at 1-1, lost the toss.
England set 279 to win, were bowled out for 217 with four overs to spare. Fast bowler Ravi Rampaul led the attack with four for 41.
Chanderpaul had moved up from No 5 after top-scoring for the West Indies with 53 not out during their 79-run defeat in Sunday's series opener at Lord's.
Together with Marlon Samuels, dropped on 14 by Paul Collingwood, the England captain, off his own bowling on his way to 77, he put on 175 for the third wicket in 34 overs.
However, England appeared to have weakened their bowling significantly by omitting Monty Panesar.
This left them without a frontline spin bowler (Panesar's replacement Michael Yardy was given just six overs) which meant their attack lacked both variety and control.
England were 30 for two inside seven overs after Alastair Cook holed out to mid-off against Daren Powell and Ian Bell, on his Warwickshire home ground, was lbw to Rampaul although the ball appeared to be going over the top.
Matt Prior and Kevin Pietersen played some typically aggressive shots as England reached fifty.
But when dangerman Pietersen was out for nine, bowled middle-stump by Rampaul as he aimed legside, England were 64 for three.
Prior completed a 71 ball-fifty, his first at this level, with one six and three fours.
But two balls later, on 52, he chipped Daren Powell to Devon Smith, running round from mid-wicket in gathering gloom.
Eight balls afterwards England were 117 for five. Collingwood, who'd just avoided a Fidel Edwards bouncer the previous delivery, was lbw for one to a full-length ball from the quick in an intelligent piece of bowling.
Owais Shah and Yardy shared a stand of 54 without threatening the run-rate before the latter pulled Dwayne Bravo to Dwayne Smith at deep square leg.
And the game was up for England when, five balls later, 171 for six became 172 for seven after Shah, on 45, edged a pull off Rampaul to wicket-keeper Denesh Ramdin.
Earlier, Chanderpaul's hundred was only his seventh in 219 ODIs.
The 32-year-old Guyanese had been a thorn in England's side during the hosts 3-0 Test series success, averaging 148.66, and this was another example of his ability to pace an innings after he took 10 balls to get off the mark.
In all he faced 122 balls with three sixes and 10 fours.
But Chanderpaul was unable to field after straining a right ankle ligament.
West Indies, after opener and captain Chris Gayle was out, saw their run-rate slow with the second fifty taking 16 overs.
However, that provided a platform for West Indies, taking advantage of the shortened boundaries, to score 102 in the last 10 overs.
Medium-pacer Dimitri Mascarenhas was England's most economical bowler with none for 31 in 10 overs.
Chanderpaul, on 43, cut Mascarenhas to backward point where Bell couldn't hold a tough, one-handed, diving chance.
Samuels's 104-ball innings, with one six and seven fours, ended when he steered Broad to Sidebottom at short third man.
There was an unsavoury incident late in the innings when James Anderson, at the end of his 10th over, appeared to shoulder-barge Runako Morton.
The series concludes at Trent Bridge on Saturday.