Former Australia vice-captain Warner is fighting for a spot in their World Cup squad after completing a 12-month suspension for his involvement in the ball-tampering scandal in Cape Town last year.
The 32-year-old showed he has lost none of his power-hitting ability as he finished unbeaten on 100 from 55 balls, which included five fours and five sixes.
Warner was playing the anchor role, while Bairstow stepped up the scoring rate to belt 114 from 56 deliveries, before falling to Indian leg-spinner Yuzvendra Chahal.
England opener Bairstow smashed 12 fours and seven sixes for his second-ever Twenty20 hundred, while Warner recorded his third consecutive 50-plus score to top the IPL scoring charts this season.
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"He's great fun, just going ahead with hitting the ball," Bairstow said of Warner after Hyderabad finished with 231-2. "It's fantastic to bat in the middle with him."
With the colossal partnership in Hyderabad, Warner and Bairstow also became the first pair to make three consecutive 100-run partnerships in the IPL.
"Must say everything about their partnership has been extraordinary. Some serious shots and hard running between the wickets in this heat. Truly remarkable," Indian batting great Sachin Tendulkar said on Twitter.
Chasing 232 to win, Bangalore lost five wickets for just 30 runs, including captain Kohli and South African talisman AB de Villiers.
Afghanistan off-spinner Mohammad Nabi finished with four wickets for Hyderabad as the hosts clinched a convincing victory.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
