Chris Jordan wrecked the West Indies top-order batting as England completed a crushing, series-clinching victory at Warner Park.
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.
Six players test negative in coronavirus retests; Pakistan announce 20-member squad
Shadab Khan, Haider Ali and Haris Rauf test positive for coronavirus
PCB conducts COVID-19 tests of five reserve players
Ross Taylor open to a possible PSL stint in the future
Seven additional Pakistan players test positive for coronavirus
Six players eligible to join Pakistan squad after second negative test in three days
'Plans underway to stage remaining PSL matches this year' - PCB
England name 30-man training group for West Indies Tests; Moeen Ali makes a return
Second group of Pakistan cricketers to leave for England on Friday
Hafeez tests negative for coronavirus a day after being declared positive by PCB