Asked to bat first by the visitors, Mumbai posted 142/8 in their allotted 20 overs and then produced a superb bowling performance to restrict Delhi to 128/7 despite a tough challenge from the South African duo of Kagiso Rabada and Chris Morris.
Coming together when Delhi was reeling at 24/6, the two added 91 runs between them.
Rabada scored 44 runs off 39 balls before being bowled by Jasprit Bumrah. The South African hit four boundaries and a six. Morris was the highest scorer among the Delhi batsmen, remaining unbeaten on 52 off 41 balls, hitting five boundaries and a six along the way.
Pacer Mitchell McClenaghan was the most successful among the Mumbai bowlers with figures of 3/24. Young pacer Bumrah returned 2/21 while Hardik Pandya notched up figures of 1/23 The Delhi batsmen had only themselves to blame for the defeat as most of them fell to poor shot selection which put the visitors under pressure early in their innings.
They had a disastrous start to their run chase and suffered a blow in the very first over when Aditya Tare was run out while attempting a quick single thanks to an excellent piece of fielding by Pandya.
McClenaghan sent back Sanju Samson in the next over when Mumbai skipper Rohit Sharma pulled off an easy catch at mid-off.
He struck twice in his next over, getting rid of Shreyas Iyer and Corey Anderson.
Iyer gloved a short-pitched delivery which was going down leg to hand an easy catch to Mumbai wicketkeeper Parthiv Patel, while Anderson was trapped leg before when he missed the line.
After Mitchell Johnson had delivered a maiden over to put more pressure on the visitors, Bumrah dismissed Rishabh Pant when the left-hander edged one to Harbhajan Singh at first slip.
There was more disappointment in store for Delhi in the next over when Karun Nair produced another poor shot, chopping at a Pandya delivery only to see the ball take the bottom edge and crash into the stumps.
Rabada and Morris then got together to give Delhi a glimmer of hope. But when Bumrah bowled Rabada to leave Delhi struggling at 115/7 in the 19th over, the match was as good as over.
Earlier, Delhi rode on an excellent bowling effort to restrict Mumbai to 142/8.
Electing to bowl, they banked on their strong pace battery of Rabada, Morris, Pat Cummins, leg spinner Amit Mishra and an electric fielding effort from Samson to remove the top four -- Patel (8), Jos Buttler (28), Nitish Rana (8) and skipper Sharma (5) cheaply.
Patel and Buttler started well by raising a 37-run partnership before South African pace sensation Rabada broke through the defence of the Gujarat southpaw, crashing his leg stump with a yorker at 145 kms per hour.
Buttler, who dispatched Morris for a consecutive six and four, was dropped on 11 the next ball by wicketkeeper Pant.
The Englishman, however, failed to seize the advantage, getting out after facing 18 balls and hitting three boundaries and two sixes, when he was brilliantly run out by a direct hit from Samson.
Coming in to bowl only in the eighth over, Cummins dealt another blow to Mumbai by getting the key wicket of Rana with his very first ball as his attempt to pull a short delivery from the Australian only ended at the hands of Corey Anderson at deep midwicket.
Before Mumbai could do much to recover from the early jolts, leg-spinner Mishra struck with the wicket of Rohit, whose poor run with the willow continued to haunt the Mumbai Indians.
Tottering at 60/4, Keiron Pollard (26) and Krunal Pandya could add only 24 runs in the next three overs before Mishra's googly ended the latter's 16-ball stay as his attempt to tickle the ball fine towards third man only resulted in a thin edge for stumper Pant to latch on to comfortably.
With half the side back in the dugout by the 13th over, Mumbai's hopes of posting a decent total rested on Pollard and Pandya (23).
The West Indian clearly looked out of touch but managed to get two boundaries in Zaheer's final over before Cummins got the better of him with a slower one off the first ball of the 18th over.
Pollard, who added 36 for the sixth wicket with Pandya, faced 29 balls and helped the ball to the ropes on four occasions.
Pandya did well to smash the ball out of the park twice but had little answer to some excellent death bowling by Delhi.
Rabada, bowling the penultimate over of the innings, displayed his football skills well to run Harbhajan (2) out while attempting a quick single before Nair effected Pandya's run out in the final over. For Delhi, Mishra and Cummins were the pick of the bowlers picking two wickets each while Rabada chipped in with one.