The 25-year-old Allen put the Super Kings to the sword in Friday's Challenger to help his side make 200-6 off their 20 overs after being inserted by Super Kings skipper Faf du Plessis.
Allen faced 53 balls and hit nine fours and five sixes on his way to 101 and was supported well by Australian wicket-keeper/batsman Josh Inglis who hit 37 off 25 balls including two fours and a six.
Afghan left-arm wrist spinner Noor Ahmad snagged 3-27 from his four overs for the Super Kings.
Then, despite unbeaten fifties from both Devon Conway and Joshua Tromp, TSK fell agonizingly short of a spot in the final, finishing 190-4 from their 20 overs.
Conway led the way with 62* off 38 balls including four fours and two sixes while Tromp hit five fours and two sixes on his way to a 36-ball 56*.
Captain du Plessis had earlier made 45 off 22 balls.
Conway and Tromp got together at 90-4 in the 10th over and tried their best with a 100-run partnership but the runs proved to be just enough for the Unicorns.
The Unicorns will now square off with the Washington Freedom in Sunday’s final, also being played at the Grand Prairie Stadium.
The pair met on Thursday in the qualifier where the Freedom chased down 146 in 15.3 overs to book their spot in the final.
The three-time champions, targeting 292 for victory, slumped to 91 for seven before turning things around thanks to Maxwell’s breathtaking unbeaten 201, which came off 128 balls and included 21 fours and 10 sixes.
It was with the last of those sixes that the 35-year-old all-rounder – who battled on despite appearing in some pain – wrapped up the win with 19 deliveries to go.
It was the highest-ever score by an Australian in a one-day international, as the team achieved the highest successful ODI run chase there had ever been at the Wankhede Stadium.
The ground had seen history made earlier with Afghanistan recording their maiden World Cup century, Ibrahim Zadran posting an unbeaten 12.
Their total of 291 for five also featured contributions of 35 not out from Rashid Khan and 30 from Rahmat Shah as Afghanistan sought to beat Australia for the first time at the fourth attempt in this format.
Australia’s reply started badly with Travis Head being dismissed for a duck by Naveen-ul-Haq with only four runs on the board.
And the wickets continued to go as Pat Cummins’ men stumbled to 49 for four after Azmatullah Omarzai took the scalps of David Warner and Josh Inglis in consecutive balls.
When Mitchell Starc was ousted – despite questions over whether the ball had hit his bat – via a superb catch from wicketkeeper Ikram Alikhil to leave Australia at 91 for seven in the 19th over, Afghanistan looked to be closing in on a famous victory.
But Maxwell then took centre stage with a stunning display to push Australia to victory.
Having been dropped and survived an lbw appeal on review, he went on to register boundary after boundary, even though at times he looked to be in considerable discomfort and struggling to run.
Able to continue after receiving treatment on the field, he subsequently completed his double-century – and Australia’s win – in fitting fashion by crashing yet another maximum that took his partnership with Cummins (12) to 202.
Third-placed Australia advance into the last four, joining India and South Africa, ahead of finishing their group matches by playing Bangladesh in Pune on Saturday.
Afghanistan remain sixth, with one of them, New Zealand and Pakistan set to make the semi-finals – they face South Africa in Ahmedabad on Friday.
Blistering half-centuries from Nicholas Pooran and Rovman Powell highlighted the West Indies' innings, propelling them to a formidable total of 257 for 4 in their 20 overs. Pooran was particularly destructive, smashing 75 from just 25 balls, including five sixes in a mere six balls against Australian spinners Ashton Agar and Adam Zampa.
Powell continued the onslaught with a quick-fire 52 from 25 balls, ensuring the West Indies maintained an aggressive tempo throughout their innings. Sherfane Rutherford added the finishing touches with an unbeaten 47 from just 18 deliveries.
Australia, struggling with a short-handed team for the second consecutive match, fielded only nine players, supplemented by coaches and selectors acting as substitute fielders. The absence of key players and the late arrival of allrounder Marcus Stoinis, whose kit was delayed in Miami, further hampered their performance.
Despite the challenges, Nathan Ellis showed promise with the ball, claiming 2 for 42 from his four overs. However, the Australian bowlers were otherwise put to the sword, with Zampa conceding 62 runs and Josh Hazlewood 55 in their respective spells.
Sent in to bat, West Indies got off to a quick start with Shai Hope and Johnson Charles laying the foundation. Pooran then took centre-stage, hitting the first three legal deliveries he faced for sixes and maintaining a high strike rate. His half-century came off just 16 balls, demonstrating his aggressive intent. Although Borovec dropped a catch off Pooran, it didn’t prove too costly as Bailey managed to dismiss him shortly after.
Powell continued the momentum with a brutal assault on Zampa and Agar, who conceded 120 runs between them. Tim David, in a rare role as a bowler, managed to be the least expensive with figures of 1 for 40 from four overs.
Chasing 258, Australia’s reply was spirited but ultimately fell short at 222 for 7. Josh Inglis top-scored with a brisk 55 off 30 balls, but the lack of depth in the batting lineup was evident. In a surprising move, Agar opened the batting and contributed 28 off 13 balls, but the rest of the lineup failed to capitalize.
David Warner, who missed the recent Australia-West Indies Test series, was bowled for 15 by Shamar Joseph after a brief flurry of boundaries. Mitchell Marsh, playing in his preferred No.3 position, was dismissed cheaply, and while David and Matthew Wade managed 25 runs each, they couldn't keep pace with the required run rate.
Gudakesh Motie was instrumental in stemming the flow of runs during the middle overs, finishing with figures of 2 for 31, including the key wickets of Inglis and David. Ellis provided some late resistance with a quick 39, sharing a 51-run stand with Zampa, who remained unbeaten on 21.
The West Indies' dominant performance, spearheaded by Pooran and Powell, sets a confident tone ahead of the T20 World Cup.
The T20 World Cup kicks off on Saturday, and the West Indies' emphatic win serves as a strong warning to their rivals as they aim for glory on the global stage.
Opener Alick Athanaze with a 60-ball 32, was the only batsman to offer any real resistance as West Indies were embarrassingly bowled out for 86 in 24.1 overs, their fifth lowest ODI score. Only Keacy Carty (12) and Roston Chase (10) were the other double figure scores in the dismal innings.
Still, Australia, playing their 1,000th ODI, the second nation to do so after India, were almost flawless following comprehensive victories in Melbourne and Sydney.
Xavier Bartlett, like he did in the first contest, again starred with the ball, as he ended with four wickets for 21 runs, after which openers Josh Inglish and Jake Fraser-McGurk raced toward the low target by smashing 67 runs within five overs, and laid the foundation for the hosts to complete their eight-wicket victory with 43.1 overs to spare in what was the shortest men's ODI ever played in Australia.
The match lasted just 31 overs and was completed in three hours, including the innings break.
Australia 87 for 2 (Fraser-McGurk 41, Inglis 35*) beat West Indies 86 (Bartlett 4-21) by eight wickets
Inglis raced to 22 off seven deliveries, as he played gorgeous orthodox shots, but was quickly overtaken by Fraser-McGurk, who muscled three sixes in four balls off seamer Matthew Forde.
Fraser-McGurk was on track for a rapid half-century, but holed out to mid-on to end his 18-ball 41 and dashed Australia's hopes for a 10-wicket win.
Aaron Hardie made just two before Australia passed the target after 6.5 overs.
Earlier, Steven Smith's decision to bowl first was aided by a shoddy West Indies effort with a number of batters dismissed in tame fashion.
Following his stunning four-wicket debut at the MCG, Bartlett was immediately on the money with the new ball, as he had opener Kjorn Ottley trapped in front in his second over.
Athanaze and Carty held firm as West Indies' fortunes momentarily seemed to turn, and they eyed a decent total on the traditionally batting-friendly Manuka Oval surface.
West Indies avoided the early collapses that marred their opening two games, but the introduction of Lance Morris in the 11th over soon left them in familiar woe.
Morris had his first international wicket when Carty was brilliantly caught by a flying Marnus Labuschagne at backward point. Captain Shai Hope unsuccessfully reviewed a leg-before-wicket decision off Sean Abbott in the next over, before Morris clean bowled debutant Teddy Bishop with a searing full delivery that rattled the stumps.
Athanaze held the innings together until he threw away his wicket with a rash sweep stroke against leg-spinner Adam Zampa that was caught at deep backward square.
Smith went on the attack and brought back Bartlett, who on his first delivery nicked off Romario Shepherd.
West Indies' woeful performance was summed up with a comical run out of Forde, who bickered with batting partner Roston Chase on his way off, as their 27-year ODI drought against Australia in Australia continues.
