Batting first after winning the toss, Royals 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.
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.
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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.
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.