Electing to bat, Hyderabad captain David Warner fell early in the second over for just four but Williamson and Dhawan treated the home supporters with some breathtaking shots to take the home side to a challenging total.
Playing in his first match of the season, Williamson was the more aggressor of the duo as he hit six fours and five sixes in his 51-ball knock before he was out in the 17th over.
Yuvraj Singh did not contribute much as he was out for three after facing four balls. Moises Henriques and Deepak Hooda remained not out on 12 and nine respectively.
For Delhi, pacer Chris Morris bowled a superb spell, grabbing four wickets while giving away 26 runs. He was on a hat-trick in the 19th overs after taking the wickets of Dhawan and Yuvraj but Hooda denied him the feat.
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New Zealander Williamson was the star of the Hyderabad innings and his 136-run partnership with Dhawan for the second wicket the highlight of the Hyderabad innings.
Williamson took 19 runs from Amit Mishra in the 14th over with two sixes in that over before being out in the 17th over.
Dhawan and Yuvraj Singh fell in consecutive deliveries in the 19th over but Deepak Hooda and Moises Henriques took 17 runs from the final over bowled by Zaheer Khan to take the score past 190.