The tourists posted 146/7 after captain Hayley Matthews' superb unbeaten century.
But England made light work of the chase by reaching the target in 16.3 overs thanks to Sophia Dunkley's brilliant 81 not out from 55 balls.
Matthews' sensational solo effort held West Indies together, with Mandy Mangru's 17 the second-highest score after they had slipped to a dismal 87/6.
She reached her 67-ball ton from the final ball of the innings, having expertly farmed the strike as the wickets tumbled around her, with England's Lauren Bell taking 2-29.
England's new-look bowling included a recall for fast bowler Issy Wong, who took 1-35, while fellow Bear Em Arlott performed admirably with 1-28 on her international debut.
The three-match T20 series continues at Hove on Friday and is followed by three one-day internationals.
Nat Sciver-Brunt, speaking to Sky Sports:"Happy days, I didn't have to do anything.
West Indies captain Matthews said:"It was a good day for myself but unfortunate not to get the win. We were 15 or 20 runs short.
"It is always pretty good to get a hundred. Hopefully, I can carry this form throughout this series."