Chasing just 82 to win, England reached their target off 9.2 overs with new Captain Nat Sciver-Brunt unbeaten on 55 from 31 balls and Sophia Dunkley scoring 24 not out.
Danni Wyatt-Hodge fell to the first ball of the innings, the only bright spark in another dismal display from the tourists and another completely one-sided contest.
West Indies slipped to 29-4 before eventually crawling to 81-9 as they had no answers to England's impressive discipline and aggression with the ball.
Seamer Arlott, in just her second international outing, finished with 3-14, including the key breakthroughs of Windies skipper Hayley Matthews for six and veteran batter Stafanie Taylor for a duck.
Pace bowler Lauren Bell took 3-28 and spinner Charlie Dean bowled a miserly spell of 2-12 from her four overs.
Shemaine Campbelle and Shabika Gajnabi were the only two West Indies batters to reach double figures, scoring 26 and 22 respectively, and only eight boundaries were scored in their entire innings, which also included 74 dot balls.
The third and final T20 takes place at Chelmsford on Monday.
Sciver-Brunt said: "We set a pretty high standard for ourselves in the first game and we probably topped that here with our performance. It's a great energy builder for us."