Bairstow led the charge at the top of the order with his best T20I score of 68 off 40 balls with two sixes and nine fours
Gayle signed off on his ODI career in the region with a blistering 77 off just 27 balls to catapult his side to victory with almost 38 overs to spare
"I just have to work on the body, and then maybe you can see a bit more Chris Gayle. Things change quickly."
Adil Rashid snared four wickets in five balls as England resisted a determined West Indies effort to claim a 29-run victory
The fourth ODI will be played at the same venue in Grenada on February 27
For all of Cottrell's heroics, it was Jason Holder who turned the match on its head with ten overs left.
Jason Roy will also miss the series to return home for the birth of his first child after the final one-day international.
Fresh from a hundred in the lone warm-up match at the weekend, Roy was at his most ruthless against the hosts who missed key fast bowler Kemar Roach.
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