Warner blasted his way to 49 off 34 balls, with the help of two sixes and seven fours, while his opening partner Dhawan made 48 in 43 balls as the two left-handers put on 81 for the first wicket in just over 10 overs.
Harbhajan, who opened the bowling had fantastic figures of 2/23 in four overs while Bumrah was once again brilliant at the death taking 3/24 in 4 overs.
Warner and Dhawan made a cautious start and then accelerated during the later stages.
The first two overs from Harbhajan and Malinga yielded just four runs before Sunrisers captain Warner struck the off-spinner for a couple fours on the off-side.
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The Powerplay overs produced 34 runs and that too after the Sunrisers skipper hit Malinga behind the wicket for two fours on either side.
The seventh over from McClenaghan was very productive with 15 runs coming off it.
It took a stunning, full length diving catch by wicket keeper Parthiv Patel after he ran some yards to his left to send back Warner off Harbhajan when the batsman attempted a reverse sweep and provide MI with the breakthrough in the 11th over.
Warner had struck a stunning six off a similar shot to the previous ball from the off-spinner who got his revenge immediately.
The crafty Harbhajan then picked up the wicket of Deepak Hooda (9) in his last over after changing ends as the batsmen went for a slog sweep trying to hit a top-spinner.
When Yuvraj Singh got out cheaply to Hardik Pandya, Mumbai Indians looked well in control with the Sunrisers under check at 123 for 4 in the 16th over.
Ben Cutting made a quick-fire 20 in ten balls with four fours but there was none to provide a late thrust once he was yorked by Bumrah who then scalped Naman Ojha and Rashid Khan too in the final over.
With MI bowlers on top, only 18 runs were scored in the last three overs.