Opting to bat first at Eden Gardens, South Africa never quite found sustained momentum despite a fighting total of 169/8.
Early jolts from Matt Henry and Cole McConchie reduced the Proteas to 12/2 inside two overs. Aiden Markram (18) and Dewald Brevis (34) attempted to rebuild, but regular wickets halted progress. Tristan Stubbs contributed a steady 29 before falling late in the innings.
The real spark came from Marco Jansen, who blasted an unbeaten 55 off 30 balls, including five sixes, dragging South Africa to a competitive-looking total.
Rachin Ravindra (2/29) and Matt Henry (2/34) were the standout bowlers for New Zealand, keeping the scoring in check through crucial middle overs.
Yet, what looked competitive on paper soon turned into a footnote in the Allen show.
Chasing 170 in a World Cup semi-final often brings pressure. Allen turned it into a power-hitting exhibition.
From the outset, Allen attacked with fearless intent. Cover drives, flat-batted pulls, and towering sixes rained down on a stunned South African attack.
Jansen’s opening spell disappeared for 53 runs in just 2.5 overs, as Allen dismantled pace and spin alike.
Tim Seifert matched the tempo with a brisk 58 off 33 balls, and the opening partnership of 117 runs effectively ended the contest inside the Powerplay and early middle overs.
Allen brought up his century in just 33 deliveries, one of the fastest hundreds in T20 World Cup history, finishing unbeaten on 100 with 10 fours and 8 sixes at an astonishing strike rate of 303.03.
New Zealand raced to 173/1 in only 12.5 overs, completing one of the most dominant chases ever witnessed in a World Cup knockout.