Chasing a challenging 180 for win, skipper David Warner led from the front scoring 52 off 41 balls while Yuvraj Singh made unbeaten 42 off just 24 deliveries as Sunrisers comfortably overwhelmed the target, reaching 183 for three in 19.4 overs.
With this win, Sunrisers are all but through to the knockouts and are currently atop the standings with 16 points from 12 games.
The loss means Kings XI became the second team after Rising Pune Supergiants to be eliminated.
But Sunrisers looked in total control throughout the chase with Warner and Shikhar Dhawan (25 off 22 balls) putting on 68 runs in eight overs for the opening stand.
A Mohit Sharma direct throw from long-on cut short the opening partnership with Dhawan falling short off the crease by a margin at the non-striker's end.
But Warner, who brought up his 50 in 38 balls, continued to build up the innings along with Deepak Hooda, who made 34 off 22 deliveries with the help of three fours and one six.
At 97/2 and needing 83 off 47 balls, Yuvraj joined Hooda at the crease.
With Sunrisers needing 50 runs in the last five overs, Hooda smashed Marcus Stoinis for two boundaries to bring down the equation.
However, Hooda departed in a bid to accelerate when he lobbed a Sandeep Sharma delivery to David Miller at deep midwicket.
(REOPENS DEL 45)
Earlier, Amla was a treat to watch as he tore apart the famed Sunrisers bowling attack. He srruck 14 boundaries and two sixes during his knock.
Amla, who brought up his 50 in just 30 balls, did not spare a single Sunrisers bowler, including young pace sensation Mustafizur Rahman.
To add to Sunrisers woes, had to pull out midway through his third over because of an injury to his right leg and his overs were later completed by Ben Cutting.
Electing to bat, Amla and skipper Murali Vijay (6) made a steady start for Kings XI before the latter fell at the team score of 33 in 4.2 overs.
Vijay was foxed by Mustafizur with slower ball that went straight to Warner at mid-off
Wriddhiman Saha (27 of 23 balls), who came in after Vijay's fall, and Amla shared 54 runs for the second wicket before Moises Henriques provided the second breakthrough when he had Saha, caught by Deepak Hooda.
Bhuvneshwar was the most successful bowler for Sunrisers returning with figures of 4-0-32-2 while Rahman had figures of 4-0-32-1.
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