Don't take Jimmy for granted - Cook

England arrived at the National Stadium in Grenada fearing a second successive draw on a stubbornly flat pitch, but Anderson turned in an unforgettable effort in a nine-wicket victory.

He played a part in all six of the wickets that fell in the decisive morning session, taking three for one with the second new ball before chipping in with two catches and a predatory run out.

England were left with a chase of 143, knocked off with ease by Cook (59 not out) and Gary Ballance (81no), the latter reaching 1,000 Test runs in just 17 innings.

But it was Anderson, who became the nation's leading Test wicket-taker in Antigua last week, who took centre stage.

"We should cherish every moment he bowls for England," Cook said.

"We turned up at the ground thinking it would be a lot of hard work on a flat wicket and it was, but when you've got special players in your team they can produce special performances at the drop of a hat.

"When Jimmy got that rhythm going I thought he would be the guy to change the game.

"I was slightly surprised with his run out and his two catches, I didn't quite know he had that in him, but it was fantastic skill and heart.

"His spell in that heat, after all the overs he bowled in this game and the last one was fantastic. It was the turning point.

"Sometimes we take Jimmy for granted because we kind of expect him to be able to swing it both ways, reverse it and never miss his length. That doesn't always happen but he's pretty close time and time again.

"I'm very lucky to have played with Jimmy and to still be playing with him."

Cook, who batted with great control to record twin half-centuries in the match, also hailed his record-breaking Yorkshire batsmen.

Joe Root pipped Anderson to the man-of-the-match award for his unbeaten 182, in the process becoming the second youngest Englishman to 2,000 Test runs after Cook himself.

Ballance, meanwhile, became the third fastest England batsman to 1,000 after greats Herbert Sutcliffe and Sir Len Hutton.

And Cook did not hold back in praising the pair.

"I haven't seen young players bat like that for England, in terms of the way they go about their business and how good they are," he said.

"I genuinely believe they're going to take English batting to a new level over the next 10 years or so.

"Credit to them for working as hard as they do and being as good as they are. Hopefully that upward curve will continue."

Victory was England's first in an away Test since defeating India in Kolkata in December 2012, with 10 games overseas taking place since then.

Root, Ballance, Ben Stokes, Chris Jordan, Jos Buttler and Moeen Ali were all celebrating their first success on the road and it is a moment Cook believes will linger in the mind.

"That's what makes it special...these are the moments you will remember when you stop playing cricket," he said.

"We probably won't remember the scores in 30 years but we'll remember sitting in that dressing room and the effort it took to win on a pretty flat wicket."

  James Anderson inspired England to a nine-wicket victory against the West Indies
James Anderson inspired England to a nine-wicket victory against the West Indies