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Experienced all-rounder Jason Holder and first-innings century-maker Nkrumah Bonner steadied the ship, surviving until the end at Viv Richards Stadium on the island of Antigua.
Holder bowled Saqib Mahmood to become only the fourth player to claim four wickets in four balls in T20 history having already secured the scalps of Chris Jordan, Sam Billings and Adil Rashid off consecutive balls.
The all-rounder will be available for selection for Friday's match against Bangladesh.
Sunrisers Hyderabad have named West Indies all-rounder Jason Holder as Marsh's replacement.
The West Indies captain hopes England will reciprocate his team's visit during the COVID-19 pandemic and tour the Caribbean later this year.
The 29-year-old became the first England player to reach the top spot since Andrew Flintoff in May, 2006.
The lanky speedster said his side has been as competitive a Test side as any despite the numbers not stacking up in his favour.
England are ahead by 170 runs with two wickets in hand at close on day four of the first Test at Southampton.
West Indies showed great discipline and rode their luck at times as they reached 57/1 in reply to England's first innings total of 204.
Earlier this month, former West Indies captains Darren Sammy and Chris Gayle said they have experienced racist abuse and threw their weight behind the Black Lives Matters campaign.