After being put into bat by Kings XI on a green looking wicket in Mohali, Sunrisers lost Shikhar Dhawan for one early on as he top-edged Mitchell Johnson (2-39) to first slip.
But 58 from 41 balls from Warner ??? with 10 fours and a six ??? helped the Sunrisers to 76 inside 10 overs before he fell to Axar Patel (2-25).
Moises Henriques (30 of 32 deliveries) and Naman Ojha (28 off 26) added 45 together for the fourth wicket but both were a little circumspect.
Ravi Bopara fell for a two-ball duck after Ojha departed and the Sunrisers were fortunate to benefit from a handy Ashish Reddy cameo as he hit 22 from eight, propelling them to 150-6 with two sixes in the final over of the innings.
The home crowd were silenced as Sunrisers reduced Kings XI to 13-2 when Boult and Bhuvneshwar Kumar (2-23) bowled Manan Vohra and Shaun Marsh respectively.
George Bailey (22 off 16) and David Miller (15 off 14) rebuilt briefly but when the latter fell in the 13th over, Kings XI were 72-5 and facing a heavy defeat.
A great knock from Wriddhiman Saha (42 off 33) again rallied the home support with only 35 needed from the final three overs, but the returning Boult accounted for him and Patel (17) in the 18th over to all but end the contest.
Only a further seven runs were added from the final two overs as Sunrisers sealed a comfortable win – their third of the tournament – keeping them in the hunt for the semi-finals.