Cook shared an opening stand of 122 with Ian Bell (53) and 81 with Jonathan Trott as the hosts chased down the tourists’ below-par 238-9 in 45 overs.
Put in to bat, the Windies failed to build on Chris Gayle’s explosive 53. Dwayne Bravo top-scored with 77 off 82 balls but the innings fizzled out with only 19 runs in the last five overs.
Their total never looked enough on a true pitch and in bright sunshine, and Cook and Bell gave a masterclass in how to chase down a modest target, picking up singles off most balls and putting away any wayward deliveries for four.
Cook was marginally the more aggressive, taking a particular liking to the off-spin of Sunil Narine, whom he cracked for successive fours on either side of the wicket in racing to a 51-ball half-century.
England were scoring at more than six runs per over when Bell, a centurion in the first match at the Rose Bowl, gifted his wicket to Darren Sammy with a loose drive to cover.
Cook marched on to reach his fourth century since taking over as one-day captain a year ago - and the sixth by an England opener in successive one-day internationals. With Trott playing his usual game of steady accumulation, Cook steamed to three figures off 114 balls.
After 12 fours, he bludgeoned his first six off opposite number Sammy over long-on before falling trying to repeat the shot and ballooning the ball up in the air.
That left Trott, who finished 43 not out, and Ravi Bopara to steer England to a victory that was even more comprehensive than their 114-run Duckworth-Lewis win in Saturday’s series-opener at the Ageas Bowl.
The second contest began in sombre mood as The Oval remembered Surrey batsman Tom Maynard, who died on Monday after being struck by a London Underground train. There was a minute’s silence before the start and players from both teams wore black armbands.
After West Indies scored just six runs in the first four overs, Gayle gave their innings lift-off. He smashed Tim Bresnan for three huge sixes and James Anderson two, with one missile clattering into the scoreboard and another almost dislodging some tiles from the roof of one of the stands.
With Lendl Simmons hardly playing a shot at the other end, it was a one-man show and when Gayle reached his fifty off 41 balls, the Windies total was 59-0. Gayle was stopped in his tracks when umpire Tony Hill took an age to adjudge him out lbw off Graeme Swann. The batsman immediately ordered a review, which appeared to show that that the ball struck pad before bat, but Gayle looked less than impressed as he reluctantly trudged away from the wicket. The dangerman gone, England seized control with three quick wickets. Dwayne Smith was caught behind aiming a heave at Stuart Broad, Simmons was run out for a 50-ball 12 by a Cook direct hit and Marlon Samuels was caught in the deep for 13.
A rebuilding job was called for and the Windies found the men for the task in Bravo and Kieron Pollard. Watchful at first, then increasingly aggressive, they added 100 in 19 overs to set the tourists up for an imposing total.
Pollard top-edged Bresnan to Anderson to fall for 42, but Bravo kept up the momentum with Sammy, who scored 21 off 20 balls.
The tourists’ innings rather petered out after the skipper’s dismissal as Denesh Ramdin and Sunil Narine fell cheaply and Bravo was caught playing one shot too many.
Tino Best strained every sinew in a bid to emulate his Edgbaston Test heroics but mostly connected with thin air in scoring seven off 12 balls. The series concludes at Headingley on Friday.
L Simmons run out 12
C Gayle lbw b Swann 53
D Smith c Kieswetter b Broad 0
M Samuels c Bresnan b Broad 13
D Bravo c Bopara b Anderson 77
K Pollard c Anderson b Bresnan 41
D Sammy c Morgan b Finn 21
D Ramdin c Kieswetter b Anderson 2
T Best not out 7
S Narine run out 2
R Rampaul not out 1
EXTRAS: (lb3, w5, nb1) 9
TOTAL: (9 wkts, 50 overs) 238
FOW: 1-63, 2-63, 3-79, 4-79, 5-179, 6-220, 7-223, 8-232, 9-237
BOWLING: Anderson 10-2-38-2; Finn 10-1-48-1; Bresnan 10-1-54-1; Swann 10-1-49-1; Broad 9-0-43-2; Bopara 1-0-3-0
A Cook c Simmons b Sammy 112
I Bell c Gayle b Sammy 53
J Trott not out 43
R Bopara not out 19
EXTRAS: (lb3, w8, nb1) 12
TOTAL: (2 wkts, 45 overs) 239
FOW: 1-122, 2-203
Bowling: Rampaul 7-0-29-0; Best 7-1-40-0 (5w); Bravo 4-0-24-0 (1w); Narine 10-1-54-0 (1nb, 1w); Samuels 1-0-11-0; Sammy 10-0-46-2; Smith 3-0-22-0 (1w); Pollard 3-0-10-0
Result: England won by 8 wkts
Series: England lead 3 match series 2-0