Kate Cross took four wickets as the hosts were bowled out for just 126 and England reached their target in 33.3 overs, Taylor finishing 55 not out.
Cross removed Kycia Knight in the first over of the match and also picked up June Ogle and the key wicket of Stafanie Taylor in her opening spell.
Natalie Sciver took three for 19 and Holly Colvin finished with remarkable figures of 10-6-7-2, including the wicket of top scorer Shaquana Quintyne for 42.
Cross finished with four for 51 after bowling Windies captain Merissa Aguillera, with Jenny Gunn taking the remaining wicket.
England lost skipper Charlotte Edwards with just 12 on the board, but Taylor and Lauren Winfield put on an unhurried 64 for the second wicket to allay any fears for the tourists.
Lydia Greenway contributed 20 to a stand of 36 with Taylor, who hit five boundaries in her half-century and was joined by Tammy Beaumont to see England over the line.
The win gives England a 1-0 lead going into Sunday's final game of the three-match series, after rain washed out Tuesday's opener.