Opener Roy made a mockery of a listless Mumbai Indians bowling attack as he hammered six fours and as many sixes in his 53 ball knock to help Delhi overhaul the home team's 194/7 for their first win of the season.
It was the third successive loss for MI and they remain without a point after three matches.
With 11 needed in the final over, Englishman Roy hammered Mustifizur Rahman for four and a six, before playing out three dot balls. Delhi needed one-run off the final ball and Roy connected it and completed the run to ensure that his side won, with Shreyas Iyer (27 not out) at the other end.
Roy and skipper Gautam Gambhir conjured up a 50-run stand for the first wicket. Roy made his intentions clear hitting a four off Hardik Pandya. He then smashed a towering six and a four off Akila Dhananjaya as Delhi raced to 23/0 in two overs.
Hardik Pandya conceded 21 runs in his second over as Roy hammered him for two consecutive sixes over long on and square-leg respectively and followed it with a four.
But Gambhir (15), failed to convert his start, as he gave a sitter to Rohit Sharma off Rahman.
Leggie Mayank Markanade was taken to task by Roy and one down Rishabh Pant (47 off 25 balls), who also played his role to perfection.
Pant did not spare Dhananjaya, hitting him for two sixes and a four as Delhi grabbed 19 runs of the 10th over. But Kieron Pollard brought MI back into the game with a stunning diving catch at long-off as Pant went back to the pavilion with the visitors at 119/2. Glenn Maxwell's (13) stay at the crease was cut short with Hardik taking a stunning catch.
Iyer and Roy ensured that there was no further damage and finally took their side home.
After Yadav (53 off 32 balls) and Lewis (48 off 28 balls) posted the century stand, their good work was continued by Ishan Kishan (44 off 23 balls). But the latter order batsmen failed to sustain the tempo and the total fell well below what the openers had promised.
Yadav and Lewis made their intentions clear by smashing a four each in the first over off Trent Boult. They brutally punished Boult as 15 runs came in his second over, with Yadav hitting two fours and Lewis striking his first six. Yadav then welcomed Mohammed Shami with a six and followed it with two fours as he made a mockery of the listless Delhi attack.
MI raced to 84/0 after the powerplay, their highest score in IPL history in the first six overs. But soon after that, Rahul Tewatia applied the brakes and send Lewis back, who was caught by Jason Roy at mid-off. Lewis smashed four fours and as many sixes.
Tewatia then trapped Surya in front of the wicket as Mumbai lost two quick wickets. Surya, who hit seven fours and a six, unsuccessfully reviewed the decision.
But Mumbai lost Rohit (18), Krunal Pandya (11) and Hardik Pandya (2) in quick succession, as Delhi bowlers made a strong comeback in middle and death overs.
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