Batting first, the visitors were restricted to 155/7 as Khaleel Ahmed (3/30) was the star.
In reply, SRH openers dominated the show, but quality bowling by DC changed the complexion of the match.
Kagiso Rabada picked up two wickets in 17th over which turned the match.
DC stun SRH to move to second spot
Bairstow and Warner shine once again
This was their fifth 50-plus stand in seven matches.
They have added scores of 118, 110, 185, 64, 33, 7 and 71.
Bairstow went past Jos Buttler (37) in terms of most fours hit in IPL 12 (38).
He became the fifth player to get past 300 runs this season.
Khaleel registers best bowling figures in IPL and other stats
Bhuvneshwar Kumar (2/33) now has 125 career IPL scalps.
Khaleel Ahmed (3/30) registered his best bowling figures in IPL.
This was also just his second career match in the T20 tourney.
Rishabh Pant needs seven more runs to get to the mark of 1,500 in IPL (1,493).
Keemo Paul (3/17) registered his best bowling figures in IPL.
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Warner scripts these records
Warner became the first player in IPL 2019 to get past 400 runs. He also surpassed Robin Uthappa in terms of career IPL fours. The Australian southpaw registered his 40th career IPL fifty. It was also his fourth fifty this season.
SRH vs DC
How did the match pan out?
DC got off to a poor start with Khaleel Ahmed doing the damage.
Colin Munro (40), Shreyas Iyer (45) and Rishabh Pant (27) resurrected the innings.
But after Pant's dismissal, DC missed out at the death to give SRH the desired advantage.
In reply, the hosts got off to a strong start, but Keemo Paul and Kagiso Rabada hit back to script the win.