After starting the day in a strong position of 202 for two, the West Indies collapsed to be all out for 307, setting England a victory target of 143.
The West Indies quickly lost their last eight wickets for just 83 runs once Kraigg Brathwaite who topscored with 118 and Marlon Samuels who made 37 were dismissed in the morning session.
James Anderson was the pick of the English bowlers, taking four wickets for 43 runs, while off spinner Moeen Ali finished with three for 51.