Chasing 182 for victory, KKR were up against it despite Nitish Rana's 47-ball 68.
Last Friday it was announced that Cameron Bancroft, the first of the banned trio to return to cricket, will captain English county side Durham after his nine-month ban came to an end in December.
As Australia started their second ODI against Pakistan in Sharjah, Warner gave a timely reminder of his ability to dismantle an attack while powering Hyderabad to a total of 3-181.
KKR were dealt a big blow ahead of the event as their two rising fast-bowlers Kamlesh Nagarkoti and Shivam Mavi were ruled out through injury.
The 32-year-old has now scored 37 IPL half-centuries, more than anyone else in the competition's history, despite missing last year's tournament following the fallout from his global ban.
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Rana was sent to open the innings as Sunil Narine faced fitness issues.
But Shankar ensured that Sunrisers had enough runs on the board with an unbeaten 40 with Manish Pandey not out on 8, while Yusuf Pathan (1) failed to get going.
With 37 half centuries, Warner has overtaken former cricketer Gautam Gambhir with whom he had till now jointly held the record of the most number of 36 half-centuries.
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The KKR required 53 runs to win the game from the last three overs and Russell made it look a cakewalk, smacking 49 not out in just 19 balls to see his side home with two balls to spare.
KKR were needed more than 50 runs in the last three overs where the game was pretty much in SRH's court. Gambhir, who led Kolkata to two titles moved to Delhi past year before stepping down as captain midway into the 2018 season after a poor start for the team. In the all-rounders department, Shakib-al-Hasan, Mohammad Nabi and Vijay Shankar will add variety.
While the opening game remained a one-sided affair, we have a significant competitive game to look forward to later today.