Delhi chased down a modest target of 126 with seven balls to spare with opener Murali Vijay top-scoring with a 34-ball 40 and captain Kevin Pietersen striking form after an injury lay-off with an unbeaten 26 to notch up their second win of the tournament.
The Pietersen-led side, playing their last match this season at the UAE, wobbled towards the end with J P Duminy (19) and Dinesh Karthik (2) falling in the 16th over at the Sharjah Cricket Stadium.
Chasing a small target, Delhi made a decent start with the opening stand between Vijay and Quinton de Kock (16) yielding 34 runs. The partnership ended with Michael Hussey pouncing a brilliant catch at point by diving full length and low to his left to remove de Kock off the bowling of Corey Anderson.
Vijay then stitched a 45-run stand for the second wicket with Duminy before he was out in the 13th over. Vijay was bowled as he went for an awful slog. He hit four boundaries and a six in his 34-ball knock.
Pietersen, who looked tentative and rusty during his knock of 16 in his first match two days back, steadied Delhi after the quick fall of Duminy and Karthik before steering his side home.
Pietersen hit two fours and a six in his 18-ball unbeaten knock. Kedar Jadhav (14 not out) hit the winning runs a four -- to take Delhi to 126 for four and hand Mumbai their fourth defeat on the trot.
Delhi will now head home to play their next match at Ferozeshah Kotla on May 3.
For Mumbai, who are yet to open account, Lasith Malinga took two wickets for 17 runs while Anderson and Rohit Sharma got a wicket each.