All-rounder Holder returned figures of 4-19, surpassing Dwayne Bravo as the highest wicket-taker for West Indies in T20Is and then hit the winning runs under pressure, lifting West Indies to their first T20 victory in seven matches.
The result extends a difficult run for the West Indies, who were coming off a clean sweep of defeats across formats against Australia earlier in the week.
Both teams will now travel to the Caribbean for a three-match one-day international series.
Mitchell Owen made an impressive debut as Australia beat West Indies by three wickets to take a 1-0 lead in the five-match T20I series.
Amid Indian strikes, PCB in huddle to decide whether PSL should continue
Jos Buttler top-scored again as England chased down an imposing target and beat West Indies by four wickets in the second T20 International on Sunday to take a 2-0 lead.
Glenn Maxwell levelled with names like compatriots David Warner, Aaron Finch, the Indian legend Rohit Sharma and England's Jos Buttler, becoming the player with the joint-fourth-highest centuries in T20 cricket.
Kraigg Brathwaite has resigned as captain of the West Indies Test team after four years in charge, Cricket West Indies (CWI) announced on Monday.
West Indies' skipper Jason Holder has called for his team to raise their game and close the gap with India in the second Test in Kingston, Jamaica.
From July 2016 to October 2019, in just 1,176 days, Kohli crafted seven double centuries, including six at home. He still holds the record for most Test double centuries by a captain and an Indian cricketer.
Injured Jason Holder replaced by Obed McCoy in West Indies squad for T20 World Cup
PHOTOS from Day 1 of the third and final Test between England and the West Indies at Edgbaston on Friday.
Images from Day 2 of the second Test between England and the West Indies, at Trent Bridge, Nottingham, on Friday.
IMAGES from the second Test between England and the West Indies in Nottingham on Thursday.
South Africa built a 239-run lead over the West Indies after the second day of the second Test on Friday to take the upper hand.
West Indies miss Anderson guard of honour as run out celebration goes too far
South Africa completed victory inside three days after bowling West Indies out for 222, having set them a target of 263 to win the match.
The home side were in desperate trouble at 56-6, but Holder embarked on an excellent counter-attack and put on 41 for the seventh wicket with left-hander Gudakesh Motie (11).
Kavem Hodge was on 11 not out and will resume on the fourth morning with Jason Holder on 13 as the hosts seek to close the gap on South Africa and deny the latter a sizeable lead that would give them a chance of victory.
Rohit Sharma closes in on Babar Azam at the top of the ODI rankings for batters
The Caribbean side will back themselves to spoil James Anderson's farewell Test after breaching Australia's fortress, The Gabba, earlier this year.
Images from Day 3 of the second Test between England and the West Indies, at Trent Bridge, Nottingham, on Saturday.
Alick Athanaze fell agonisingly short of a maiden Test century but still did enough to help ensure a draw in the first Test against South Africa.
Shamar Joseph has only played three T20 matches in franchise-based leagues and has not taken a wicket.
Glenn Maxwell's breathtaking knock helped Australia clinch the three-match T20I series with a second consecutive win on Sunday
IMAGES from Day 2 of the first Test between England and the West Indies, at Lord's, London, on Thursday.
Photos from the 2nd Test between England and West Indies at Trent Bridge on Sunday
India will square off against West Indies in the second T20I on Sunday.
England were in command on 30/1 at tea after bowling West Indies out for 121 on the opening day of the first Test.
'Hopefully, the South Africa series has woken up the Australian media to the realities of what it's like to operate Test cricket, and unless the boards change the economic model, I don't think Test cricket will thrive outside of the Big Three.'
David Warner became Australia's first player from the nation to make 100 appearances in all formats of cricket
'They will have to choose international cricket over one or two franchise leagues.'
Lead men's team selector Desmond Haynes said Holder and Joseph are key players for the West Indies and the decision was taken in the best interest of the side.
Fast bowling sensation Shamar Joseph should be fast-tracked into the West Indies squad for the home T20 World Cup in June, said former captain Chris Gayle.
Centuries by skipper Shai Hope and Nicholas Pooran and great spells by Jason Holder, Alzarri Joseph and Akeal Hosein helped an all-round West Indies clinch a 101-run win over Nepal.
Nicholas Pooran, Jason Holders and Kyle Mayers have declined to join the West Indies roster for the 2023-24 season.
More than eight years after Carlos Brathwaite's four sixes at Eden Gardens gave them their second T20 world title, a wounded West Indies will look to redeem themselves at home when they begin their campaign in the event's ninth edition by taking on Papua New Guinea, in Georgetown on Sunday.
While Rahul hit just one six during his knock, one could say he would remember it for a long time.
Pat Cummins confirmed Australia's new-look batting line-up on Tuesday with Steve Smith to open and Cameron Green at number four in the team to face West Indies in the first Test at Adelaide Oval from Wednesday.