Anderson ripped through the West Indies middle order in the opening session of the fifth and final day, making excellent use of the new ball to record figures of four for 43.
The Lancastrian also claimed two catches and ran out Jason Holder as the home team were bowled out for 307.
That left England chasing a small target of 143 to win and captain Alastair Cook (59 not out) and Gary Ballance (81 not out) saw them home.
Meanwhile, West Indies captain Denesh Ramdin said he was hopeful that all-rounder Jason Holder would be fit for the third and final test against England in Barbados on Friday.
Holder fell badly in his delivery stride, turning his left ankle, as West Indies slumped to a nine-wicket defeat to the tourists on Saturday.
Although the promising Bajan was stretchered off the field, evidently in some pain, Ramdin said the initial analysis was that the injury was not as bad as it seemed.
“It's just a slight injury. Hopefully he can rest up for the next few days and come back stronger,” said Ramdin.
It was a tough loss for West Indies who had batted well on the fourth day, with Kraigg Brathwaite scoring a century to set up a chance to save the test and force a second straight draw.
But the early loss of Brathwaite and five others before lunch radically shifted the balance of power.
“After four hard days of cricket, to lose the match in one session is really hard but that is how it goes,” said Ramdin.
“England went out and executed their plans and they had the conditions in their favour as the game went on,” he said, referring to England's winning of the toss which allowed them to put West Indies in to bat in overcast, humid conditions.
England paceman James Anderson took three wickets before lunch with an excellent spell which proved to be too much for West Indies to cope with.
“We fought hard for the first four days but losing six wickets in that session cost us the test,” said Ramdin.
“You should take the initiative but James Anderson took it away from us.” – Reuters
Original source: Fairytale day for England