Pacers Jaydev Unadkat (2/29) and Wayne Parnell (1/17) and spinner Shahbaz Nadeem (1/19) shared four wickets to strangle the Mumbai batting unit in their stipulated 20 overs after skipper Rohit Sharma won the toss and decided to bat.
Skipper Kevin Pietersen employed a spin-pace attack early on with Nadeem and Mohammad Shami starting the proceedings for Delhi, followed by J P Duminy and Wayne Parnell.
Mumbai Skipper Rohit Sharma (4) was the first to walk back to the pavilion when his attempt to steal a quick single ended up with a runout orchestrated by pacer Shami in the second over.
Mumbai could just manage 37 for the loss of two wickets in the powerplay. Runs dried up further and the mounting pressure took a toll on Ambati Rayudu (14) when his lofted shot off Nadeem found Laxmi Shukla at long-on.
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In the 11th over, Michael Hussey (10) brought up the fifty for Mumbai with a single but he too could not stay longer and was sent back to the hut by a slower yorker in the 14th over as Mumbai lost half of their side with 63 on board.
Pollard brought up the first six of the innings in the 16th over when he sent Shami sailing over long-on, while Gautam blasted successive boundaries off Unadkat in the 17th over.
In the next over, Pollard tried to steal a non-existent double but it ended with Gautam losing his wicket.
The West Indies all-rounder then smashed a four and a six off Shami, while Harbhajan singh (10) blasted a four and six to help Mumbai put a modest total on board.