KKR chased down SRH's target of 143 with two overs to spare and seven wickets in hand.
Chasing 143 to win, KKR rode on opener Shubman Gill’s unbeaten 62-ball 70 and Eoin Morgan’s 29-ball 42* to overhaul the target with two overs to spare.
Speaking after the match, Morgan said this win will help KKR gain some momentum and confidence as the 52-day long event progresses.
"Nice feeling to get a win under our belt. It's a long tournament, but obviously, this win helps us get some momentum and confidence going," he said at the post-match presentation ceremony.
Earlier, KKR restricted SRH to a modest 142/4 on the back of brilliant spells from Pat Cummins (1-19), Varun Chakravarthy (1-25) and Sunil Narine (0-31).
"We were a bit rusty in our last game against MI, but we won this match with our bowlers, they did a great job restricting a very strong Sunrisers batting line-up.
"Wickets of Bairstow and Warner at the top put us in a good position. They put them on the back-foot and we knew we didn't have to put ourselves under pressure in the chase," Morgan said.
In the chase, KKR were 53/3 at one stage before Gill and Morgan forged an unbroken partnership of 92 runs to see the team over the line.
Sharing his experience of batting with Gill, Morgan said: "I didn't have to tell him a great deal, to be honest, he's beautiful to watch on the eye, good bat swing, very languid style, magnificent to watch, he's good kid, very hungry to learn and I would love to bat with him once again."
KKR will face Rajasthan Royals (RR) in their next game on September 30 in Dubai.