The visiting team took early control of the Maharashtra state Derby by reducing MI to 30 for four during power play and then 68 for seven before Harbhajan Singh led the fight-back with a breezy innings of 45 not out in 30 balls to help the hosts reach 121 for eight.
The Supergiants made a fantastic start in the run-chase with openers Ajinkya Rahane (66 not out) and Faf du Plessis (34) pushing the score to 78 in 10 overs.
There was no stopping the visitors' charge after this splendid start and the Supergiants surged to victory in 14.4 overs with Rahane remaining unconquered on a well-made, unbeaten half ton off 42 balls, embellished with three sixes and seven fours, along with Kevin Pietersen (21 not out).
Rahane finished off the game in style, by striking two sixes in 15th over from Hardik Pandya.
MI, thus, made another unpromising start to their campaign after having lost five and four games initially in the last two seasons respectively.
Opting to bat first after winning the toss, MI lost their top four batsmen with only 30 on board, including captain Rohit Sharma, and then slid further into difficulties before they were revived by Harbhajan's late hitting.
India's Test pace spearhead Ishant Sharma and Australia's Mitchell Marsh struck twice each to reduce MI to 30 for four inside the six-over of power play.
MI could not recover from these early shocks and stuttered along but managed to avoid being shot out below their lowest score at this venue – 92 against Delhi Daredevils in 2012.
Among the frontline batsmen only Ambati Rayudu (22 in 27 balls) reached double figures.
Later, Harbhajan used the long handle to make an innings-high 45 not out in 30 balls, inclusive of one six and seven fours.
Harbhajan also added 28 runs, the highest of the innings, with R Vinay Kumar (12) for the eighth wicket and 25 for the unfinished ninth with Mitchell Mclenaghan.
For the league debutants, Ishant (2/36) and Marsh (2/21) did the early damage.
Rajat Bhatia (1/10) and leggie Murugan Ashwin (1/16) also got among wickets along with Ravichandran Ashwin (1/7), who was brought on to bowl his first and only over after 15 overs, and R P Singh (1/30).
In reply, the Supergiants got off to a fast start, raising 57 by the end of the six overs of power play.
While Rahane played in his elegant fashion, driving with elan, Du Plessis used his power to clobber three sixes, two of those in successive balls in the last over of power play bowled by Jasprit Bumrah, who leaked 20 runs.
Rahane started the run-flow by cover-driving Mitchell McClenaghan for a four and then hooked his short ball for a six that was later replicated by Du Plessis who stepped out and clobbered the New Zealander for a maximum over the straight field.
The South African WT20 skipper was, however, lucky to escape being run out after a misunderstanding with Rahane while going for a second run.
He was later dismissed by Harbhajan, bowled behind his legs when attempting to hoist the off spinner over the mid wicket region. But by then the Supergiants were well on way to victory.
Harbhajan (1/24) was the lone wicket taker although he was clubbed over the long-on fence for two huge sixes by Kevin Pietersen.
Brief Scores
Mumbai Indians: 121 for 8 in 20 overs (Harbhajan Singh 45 not out, Ambati Rayudu 22; Mitchell Marsh 2/21).
Rising Pune Supergiants: 126/1 in 14.4 overs (Ajinkya Rahane 66 not out, Faf du Plessis 34; Harbhajan Singh 1/24).
Rising Pune Supergiants beat Mumbai Indians by 9 wickets.