Tendulkar carried his bat, slamming an unbeaten 59 to help his side post 165 for seven.
Chennai made a good fist of the chase thanks to Matthew Hayden's 44, but fell short and eventually ended with 146 for seven.
After Mahendra Singh Dhoni had won the toss and asked Mumbai to bat, Sanath Jayasuriya and Tendulkar began briskly, tucking into opening pair of Manpreet Singh Gony and Thilan Thushara.
The two helped Mumbai reach 27 in just four overs, forcing Dhoni into a bowling change which saw the introduction of Andrew Flintoff.
The England all-rounder almost struck in his first over when Tendulkar looked to have edged the ball, but Hayden at first slip failed to hold on to a straightforward take.
