After riding on Ajinkya Rahane's unbeaten 54-ball 68 to post a formidable 179 for three, Rajatshan bowled out Mumbai for 92 in 18.2 overs.
The victory helped Rajsthan leapfrog to the top of the poinst table with four wins from five matches, while Mumbai slipped to the fourth position.
While Rahane led Rajasthan's batting, the bowling was more about team effort, with James Faulkner leading the way with three wickets.
Ajit Chandila and Stuart Binny picked up two wickets apiece.
Mumbai had a disastrous start as they lost Sachin Tendulkar in the first over, top-edging Ajit Chandila to the fine-leg fielder.
It was double delight for the home side as off-spinner Chandila struck again, having the woefully out-of-form Ricky Ponting caught and bowled to leave Mumbai, chasing a daunting target, reeling at 10 for two.
Sidhhart Trivedi had Rohit Sharma caught at mid-wicket in a rather soft dismissal, pushing Mumbai further onto the backfoot.
After failing to contribute with the bat, Binny made up with a beauty of a delivery that knocked down Kieron Pollard's middle stump, helping the hosts inch closer to a big win.
At the end of 10th over, Mumbai were staring down the barrel at 42 for four, needing another 138 runs with the required rate going up with each delivery.
Despite boasting one of the best batting line-ups in the tournament, Mumbai could manage just three fours in the first 10 overs.
And even Karthik, going through a purple patch of sorts in the league, could not get going in the face of some disciplined bowling by Rajasthan.
There was some confusion when Ambati Rayudu and Harbhajan Singh found themselves at the same end after the former, who was on strike, crossed over for a single which Harbhajan was never interested in.
The run-out decision went against Harbhajan as he stepped out of the crease and his bat was in the air when the ball hit the stumps. The rest fell in quick succession to hand Mumbai their biggest IPL loss in terms of runs.
Earlier, Rahane top-scored with an unbeaten knock to help his side post a formidable total.
Batting first after winning the toss, Rajasthan raced to fifty in only six overs and were 88 for one at the end of 10th, before the home side picked up 19 runs in the last over of the innings to put up a challenging score.
Rahane and Brad Hodge (27 off 15) added an unbroken 53-run stand for the fourth wicket in less than five overs to give Rajasthan the much-needed impetus after slowing down a bit in the third quarter.
Rahane smashed eight fours and a six during his knock and was well-supported by Shane Watson (31), with whom he added 62 runs for the opening wicket, and Dishant Yagnik (34).
Rajasthan were off to a flying start with both the openers, Watson and Rahane, looking in ominous form.
After an economical first over by Mitchell Johnson, Rahane got into the groove with a couple of boundaries off Lasith Malinga.
That was just the beginning as what followed in the next few overs at the Sawai Man Singh Stadium was nothing short of a mayhem.
If Watson signalled his intention with a massive six over mid-wicket, Rahane danced down the wicket to loft Pragyan Ojha for a maximum.
Watson meted out special treatment to Malinga, smashing the slinger for three boundaries in the sixth over, which saw Rajasthan score 16 runs.
Ojha bowled a tight seventh over, but Mumbai reaped the reward in the next over, when Keiron Pollard, releasing the ball from way behind the popping crease, forced Watson to edge a wide delivery for wicketkeeper Dinesh Karthik to do the rest.
They might have lost a big wicket but Rajasthan continued to bat aggressively, with Dishant Yagnik playing some impressive shots before being dismissed by Harbhajan, who was earlier swept for a four by the batsman.
The 29-year-old Yagnik was particularly severe on Pollard who smashed for a six and four, conceding 16 runs in the 10th over.
Much to Mumbai's chagrin, Dhwaan bowled a long 12th over, thanks to two no-balls and a wide, and ended up conceding 13 runs.
Trying to be over adventurous, Yagnik attempted to reverse sweep Harbhajan only to give a catch to Sachin Tendulkar at short fine-leg.
Rahane along with Hodge then propelled the hosts after Mumbai seemed to have checked the flow of runs a bit.