Victory, in their last Test before the start of July´s Ashes campaign, meant England took the two-match series 2-0 after a thumping 10-wicket win at Lord´s and saw them regain the Wisden Trophy they´d lost in the Caribbean this year.
The West Indies, following on, were bowled out for 176 in their second innings, having made 310 first time around after England had piled up 569 for six declared in a match where the whole of Friday´s second day was washed out.
"We came back to England after the West Indies tour keen to make amends for what went on over there," England captain Andrew Strauss told Sky Sports.
"We knew the conditions would help us a little more over here, but we played well and it bodes pretty well," he said after his side had won this series inside eight days´ playing time.
"You have to savour your Test match victories and we are delighted but we realise we have further to go as a side."
Anderson added: "I´m delighted with how it´s going. It swung around today luckily and I´m glad we could finish them off quite quickly."
West Indies captain Chris Gayle, whose side now face England in a three-match one-day series starting at Headingley on Thursday, said: "We are very disappointed with the way it worked out in difficult conditions for us but I guess it´s a great way to start the summer for England.
"We found the conditions very tough but we also played poor cricket so we can´t have any excuses."
West Indies were 167 for eight at lunch on having lost five wickets in the day´s first session after resuming on 115 for three.
And after the break the match lasted just three overs.
Star batsman Shivnarine Chanderpaul fell for 46 when he edged man-of-the-match Anderson through to Paul Collingwood, who took his first Test catch as a wicket-keeper having taken the gloves on Sunday after Matt Prior sustained a finger injury.
And Tim Bresnan, who before lunch had taken his first two wickets in Tests, ended the match when he had Fidel Edwards caught at fine leg by substitute fielder Karl Turner, who was appearing in front of his home crowd.
Anderson, who took four for 38 in this innings, had match figures of nine for 125 - his second-best in Tests after his nine for 98 against New Zealand at Trent Bridge last year.
Bresnan had an innings return of three for 45 in 14 overs.
West Indies, who resumed Monday on 115 for three, lost five wickets in the first session.
Anderson, the only other bowler used alongside Bresnan on Monday, added three more wickets before lunch to his first innings haul of five for 87, including left-hander Suliemann Benn whom he bowled for nought off the final ball before lunch.
After a pair of rain breaks saw nearly half an hour lost, the West Indies lost three wickets for five runs in 15 balls with Bresnan, in his second Test, taking two for none in three balls.
Lendl Simmons was out for 10 when he guided Anderson straight to substitute fielder Scott Borthwick at point to leave the West Indies 141 for four.
And they had added just one run when seamer Bresnan, who´d seen some chances missed off his bowling, took his first Test wicket with Nash clipping him straight to square leg where Durham´s Borthwick took his second catch.
Bresnan, who along with Graham Onions made his Test debut at Lord´s, then reduced West Indies to 146 for six.
Denesh Ramdin, who made a first innings fifty, exited for nought when he edged a genuine outswinger from the 24-year-old Yorkshireman to Anderson at third slip before Anderson himself bowled Jerome Taylor.
England had been in charge here from the start with opener Alastair Cook´s Test-best 160 the centrepiece of their total.
Ravi Bopara, who made 108 and helped Cook add 213 for the second wicket, was named man of the series after he made a Test-best 143 at Lord´s.
Related story
England may join Windies in potential BLM protest - Anderson
