Chasing a modest 146 for a win, the Warriors overhauled the target with eight balls to spare with Finch playing sheet anchor with a 53-ball 64 at the Subrata Roy Sahara Stadium to give the home side their first win in three matches.
The Warriors romped home easily on the foundation laid by the openers -- Finch and Robin Uthappa (32 off 16 balls) -- who raised 58 runs in just 4.5 overs.
Yuvraj took some time to open his account but he ended the contest in style with a six off Sreesanth as the Warriors reached 148 for three in 18.4 overs. Yuvraj's 23-ball knock was studded with two fours and as many sixes.
Finch, who hit six fours and three sixes in his knock, and Uthappa destroyed the confidence of the Royals opening bowlers Harmeet Singh and S Sreesanth with a flurry of fours and sixes early on.
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Uthappa then launched an amazing attack on Sreesanth with two sixes and a four in the pacer's next over as the Warriors reached 50 in the fourth over itself with the help of four fours and as many sixes.
The opening stand was broken in the fifth over with the Royals captain Rahul Dravid taking a brilliant one-handed catch at short-midwicket to dismiss Uthappa off James Faulkner. Uthappa's 32 came from just 16 balls and was studded with three fours and two sixes.