This is the second CLT20 title for the IPL-6 winners, having won the 2011 edition.
Chasing a massive 203-run target, Royals folded for 169 even after a fabulous start that saw them scoring 100 runs in nine overs.
Tendulkar and Royals skipper Rahul Dravid, both of whom having announced quitting the T20 game after today's match, were out for low scores.
Despite openers Ajinkya Rahane (65) and Sanju Samson (60) chipping in with quickfire half-centuries, Mumbai Indians bowlers came up with impressive bowling performance towards the fag end of their innings to have the last laugh.
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From 155 for three in 16 overs, the Royals collapsed dramatically to lose as many as six wickets for just 14 runs.
Earlier, Mumbai Indians batsmen fired in unison to post 202 for six.
After a solid start by opener Dwayne Smith (44) and a valuable 33 off 14 balls by skipper Rohit Sharma in the middle, Glenn Maxwell's 14-ball 37 cameo in the end took the IPL champions past 200-run mark.