Chasing an improbable target of 208, Mumbai were restricted to 170 runs for nine wickets in the allotted 20 overs.
Main scorers were Ambati Rayudu (62 off 39 balls with three sixes and five fours) and Dinesh Karthik (40 off 28 balls with seven fours).
Left-arm spinner Shahbaz Nadeem, and pace bowlers Umesh Yadav and Irfan Pathan got two wickets each for Delhi.
Earlier, sent into bat by Mumbai Indians captain Harbhajan Singh, Delhi Daredevils piled up a massive total of 207 for the loss of five wickets in 20 overs.
This was the second highest total by any team in the tournament after 208-5 by Chennai Super Kings against Royal Challengers Bangalore some two weeks ago.
Captain Virender Sehwag smashed 73 from 39 balls hitting four sixes and eight fours – his third successive fifty - and later was declared the Man-of-the-Match.
Mahela Jayawardene of Sri Lanka and Kevin Pietersen of England also hit half-centuries – Jayawardene made 55 with eight fours and Pietersen scored an unbeaten 26 ball-50 with three sixes and six fours.
For Mumbai, left-arm spinner Robin Peterson of South Africa claimed three wickets for 37 while Sri Lankan fast bowler Lasith Malinga took two for 31.
Geo Super showed this match live from Delhi.
