At 105 for two in the 13th over it appeared as though they were well set for a highly competitive total, with Richard Levi on 42 and providing the odd hint that he could be coming to terms with spin - his nemesis in the tournament.
However, when Levi slapped a half-tracker from Glenn Maxwell straight back at the bowler to be well caught, the Cobras innings unravelled in spectacular fashion.
With nobody able to stop the slide, the Cobras were bowled out for 135 with nine deliveries left unused as left-arm spinner Akshar Patel took 3 for 15 and medium pacer Anureet Singh took 3 for 12.
The excellent start provided by Hashim Amla (40 off 22 balls), who at one stage hit five consecutive fours, had been thrown away.
Needing less than seven runs per over, the Kings XI went about their chase methodically, although they found themselves occasionally pegged back by Robin Peterson.
The left-arm spinner’s canny bowling brought him the wickets of openers, Virender Sehwag and Manan Vohra, who both made 23, and he conceded just 19 runs from his four overs.
Sybrand Engelbrecht found himself on the receiving end of Maxwell’s hefty blade before having the last laugh, but even the Australian’s downfall was unlikely to change the course of the match.
Wriddhiman Saha enjoyed an excellent night with the gloves, effecting two sharp stumpings and taking a good catch, and he guided his team home with an unbeaten 42.
David Miller hit the winning runs to finish 16 not out as the Kings XI won with 11 balls to spare to take their place in the semi-finals.