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.
Faf du Plessis, whose stint with Kings last year was cut short due to injury, has been retained. Namibia allrounder David Wiese and Sri Lanka batter Bhanuka Rajapaksa are also among the overseas retainees.
Kings have 12 confirmed players for the season and will have five spots to fill at the draft in July.
They have retained the core of Caribbean players, which includes Johnson Charles, Alzarri Joseph, Roston Chase, Matthew Forde and Khary Pierre. Fast bowlers Shadrack Descarte and McKenny Clarke round out their retentions.
Colin Munro, who was named du Plessis' replacement last year, has been released as have Sikandar Raza, Sean Williams and Chris Sole.
Klaasen has been in phenomenal form in T20s since 2023. He finished as the second-highest run-getter in the SA20 earlier this year and was in top form in the IPL as well with 479 runs in 16 games. His strike rate in the format since 2023 is 176.80. This will be Klaasen's second stint in the CPL, having represented Guyana Amazon Warriors in 2022 where he made 118 runs in five games.
Kings made their fourth consecutive playoffs spot in 2023 but lost in the Eliminator against Jamaica Tallawahs.
The 2024 edition of the CPL is set to run from August 30 to October 7. Kings will open their campaign against St Kitts and Nevis Patriots on September 1 in Basseterre.
India started their Super 8s campaign in style in Barbados, with Suryakumar's 28-ball 53 propelling them to 181-8 from their 20 overs.
Virat Kohli added 24, with Hardik Pandya contributing a useful 30 too, though Fazalhaq Farooqi, the tournament's leading wicket-taker, finished with impressive figures of 3-33.
Yet Farooqi was outshone by Bumrah, who was the star of India's bowling attack.
Bumrah took 3-7 as he skittled through Afghanistan's top order, reducing them to 23-3 inside five overs.
Arshdeep Singh (3-36) rounded matters off, sending Rashid Khan, Naveen-ul-Haq and Noor Ahmad packing to bowl Afghanistan all out for 134.
The victory sent India to the top of Group One, ahead of Australia's clash with Bangladesh.
Data Debrief: More history for Kohli
Kohli might have taken a backseat in this win, but his haul of 24 saw him move onto 4,066 runs in T20Is.
That makes Kohli India's record run scorer in the format, with the 35-year-old having surpassed Rohit Sharma (4,050).
