Sachin Tendulkar smashed an unbeaten 89 off 59 deliveries as Mumbai Indians recovered from early jolts to post 174 for five after being sent to bat.
Rajasthan Royals were then restricted to 137 for eight that also snapped their all-win record at home.
Shane Warne's team has made a courageous comeback in the tournament but Sunday night lost to a better opponent.
They were never really in the hunt and lost wickets from the start. Three run outs then broke the back of Royals' middle order and their only hope was big-hitter Yusuf Pathan.
In Image: Sachin Tendulkar and Harbhajan Singh of the Indians celebrate the wicket of Yusuf Pathan