Klaasen smashed 74 off just 30 balls (3x4, 7x6) to power DSG to 211/6. The Proteas superstar was well supported by Wiaan Mulder, who struck an equally rapid unbeaten 50 off just 23 balls (3x3, 3x6).
DSG debutant, Bhanuka Rajapaksa, also made a solid contribution in his first outing in the competition with 35 off 23 balls.
The Super Kings had done well to reduce DSG to 94/4 after 12.1 overs with left-arm seamer Nandre Burger (2/27) delivering a fiery spell upfront.
Klaasen and Mulder take the game away
But that's when Klaasen and Mulder began their work as they added a mammoth 101 runs in just 38 balls for the fifth wicket to take the game away from the Super Kings.
The JSK run chase was always going to be dependent on their captain Faf du Plessis, but once he departed early after being caught by Quinton de Kock, who took a good catch running back to boundary, the home team's mountain became so much steeper.
It was a valiant effort after they had won their Eliminator just 24 hours earlier to give themselves the opportunity of qualifying for the final.
Moeen Ali (30), Reeza Hendricks (27) and Donovan Ferreira (24) all struck cameos for the Super Kings, but nobody could match Klaasen’s sheer brute force of earlier in the day.
The DSG bowlers backed up their batters’ pyrotechnics with a complete performance in the field and with the ball.
Dala leads the way
Junior Dala led the way again with 4/38, with Naveen (2/27) and Dwaine Pretorius (2/17) providing good support.
The catching was also out of the top drawer, highlighted by Naveen-ul-Haq’s two-handed spectacular grab at mid-off.
They will now return to Cape Town for the final in a rematch with the Sunrisers at Newlands on Saturday.