Chasing an imposing 315 for victory in the second semi-final, West were struggling at 174 for six when Yadav (80 in 56 balls with 4 sixes, 7 fours) and No.8 batsman Patel (64 not out in 38 balls) got involved in a match-winning stand of 70 runs off 76 balls.
The seventh-wicket duo added a whopping 67 runs in the batting power play that turned the side's fortunes.
Fittingly, the Gujarat youngster, who has made a good impression in the series against Sri Lanka recently, hit the winning hit - a straight six - to complete a memorable win at the Wankhede Stadium.
Top-order batsmen Sheldon Jackson (51) and Ambati Rayudu (54) had put on 89 runs in 91 balls for the second wicket but following their dismissals in quick succession, the hosts fell into trouble before Yadav and Patel bailed them out.
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Earlier, South's top-order feasted on some wayward bowling after being put in to bat by West and they piled on 314 for six.
Half-centuries from Mayank Agarwal, Baba Aparajith, Manish Pandey and a well-made 47 by opener Robin Uthappa contributed in the imposing total.
In the morning, South got off to a rollicking start on the placid track with openers Agarwal and Uthappa taking a heavy toll of some poorly directed bowling from West medium pacers Dhawal Kulkarni and Thakur to put on a stand of 104 and lay a solid platform.