Nat Sciver scored 82 to lead England to 154/6 before their bowlers controlled the chase to secure a 20-run victory despite Deandra Dottin's 62.
The result means that England lead the series 3-0 with just two games left to play.
After choosing to bat first, England found themselves in trouble early on as Shamilia Connell dismissed openers Tammy Beaumont and Danni Wyatt in the space of an over.
Sciver combined with captain Heather Knight for a 59-run partnership to steady the innings before Stafanie Taylor drew a thin edge from Knight on 29.
Amy Jones was bowled through the gate by Hayley Matthews for just 4, but Fran Wilson provided support as Sciver began to up the run rate.
Deandra Dottin, bowling in an international match for the first time since February 2019, finally dismissed the No.3 for 82 in the last over. Katherine Brunt hit her first ball for four but was bowled by her second, to leave Dottin with two wickets from her three overs.
West Indies had made two changes to their line-up from the second T20I, and they also made changes to their batting order, with Matthews dropping down the order to make way for Lee-Ann Kirby at the top.
The change didn't pay off though, with Kirby stumped for 3 off a wide by some sharp keeping by Amy Jones off Sciver. Shemaine Campbelle, promoted to No.3, also fell cheaply, failing to clear mid-off off Brunt.
Despite those wickets, the chase got off to an alright start, thanks to some booming shots from Deandra Dottin. She combined with Matthews to keep in touch with the chase, though frequent dot balls hampered their attempts to control the game.
Sarah Glenn continued her recent form to trap Matthews in front in the 13th over, and then dismissed Chedean Nation in the same manner in her next over.
With the required rate climbing out of control, the final nail in the coffin came when Wilson held on to a catch in the deep off Brunt to dismiss Dottin for 62, her second half-century of the series.
Taylor and Chinelle Henry batted out the remaining overs to take West Indies to 134/5, their highest total of the series so far.
The fourth T20I will be played on Monday, 28 September at the same ground.
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