The Warriors defended their total of 129 for nine with a clinical bowling effort on a Wankhede strip that assisted the spinners and pacers alike, restricting Mumbai to 101 for nine in the allotted 20 overs.
The visitors reduced the home team to a sorry five for three at the end of the second over and tightened the noose gradually to come out on top.
Missing an injured Sachin Tendulkar, there was little of note in the Mumbai innings, barring Dinesh Karthik's 32 off as many balls and an identical effort from James Franklin.
Both the batsmen added 49 runs for the fourth wicket.
Mumbai skipper Harbhajan Singh, who had bowled well for the wicket of his rival counterpart Sourav Ganguly earlier, made a valiant 16 off 15 balls towards the end.
Dinda, the Warriors' new recruit from Bengal, grabbed two wickets in his first over and then came back to add two more to finish with admirable figures of four for 18.
The spinners - Murali Kartik, Marlon Samuels and Rahul Sharma - choked up the Mumbai batting with the turn they got out of the pitch.
Karthik got two for 14, including the important wicket of Karthik when the game was wide open, while West Indian Samuels and leggie Sharma got a wicket apiece along with South African pacer Wayne Parnell.
Earlier, bowling effectively to a plan and fielding brilliantly, the hosts restricted the visitors to a modest total.
The Warriors, who had won only four games in the previous season, commenced their campaign on a poor note after being put in to bat. They slumped to 27 for three by the fifth over and never recovered from the big blows.