England took regular wickets to restrict West Indies to 71-8 (Merissa Aguilleira 21) with superb bowling from Holly Colvin (2-5) and Katherine Brunt (2-16). Charlotte Edwards (27 not out) and Marsh (31) led England in the run chase as the home side eased to victory in the 10th over to finish on 72-2.
The second T20 of the series will be played at Old Trafford on September 10 before England men take on South Africa.
Player of the match Laura Marsh said: “It was great to start the series off like that.
"We’re really pleased with our performance today, the opening bowlers bowled brilliantly and the spinners backed them up. We followed up well with the bat to get the job done in the 10th over.
“We’re all looking forward to carrying this momentum forwards to Old Trafford on Monday.”