Wicketkeeper Sarah Taylor hit 53 from 37 balls and Arran Brindle an unbeaten 42 from 41 as the hosts posted 150 for three, the pair having put on 78 for the third wicket.
England then impressed in the field with Anya Shrubsole making a brilliant one-handed diving catch to remove Shanel Daley and Susie Rowe making a fine effort in the deep to dismiss Britney Cooper.
Cooper had hit 20 in a stand of 40 with captain Merissa Aguilleira (37) for the fifth wicket, but the tourists were never in contention despite some late hitting from Shemaine Campbelle.
Brindle, Laura Marsh and Danielle Wyatt each claimed two wickets for England.
Player of the match Taylor said: “We got off to a great start today. I was really pleased to find the boundary early and then ran hard with Arran later on.
“It was another good team performance with everyone contributing and two outstanding catches from Anya and Susie; we pride ourselves on our fielding.
“We aim to put a marker out in every single game and we’ll be looking to do that in the remaining three matches of this series.
"We’ll take momentum from today’s performance with us onto Northampton on Thursday.”