The burly Victorian clobbered 67 off 45 balls with 10 fours and two sixes but the momentum provided by him was gone with his dismissal having added 96 for the opening stand with Robin Uthappa (26).
However Steven Smith tried his bit with a brilliant cameo smashing 39 off only 16 balls (3x4, 3x6) with a breathtaking reverse swept six off Dwayne Bravo's bowling.
Chris Morris was the pick of the CSK bowlers with 2 for 25 from four overs.
Finch, who has been the chief architect of Pune's victory against Rajasthan was in red-hot form as he got 13 runs from Dirk Nannes' opening over which included three boundaries.
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When left-arm spinner Ravindra Jadeja bowled short and wide outside off-stump, he was in position to play the cut shot as well as backfoot cover drive. Similary when Nannes or Morris bowled short-pitched stuff, Finch was quickly in a position to play the pull-shot.
He completed his 50 off 32 balls with a top-edged pull-shot off Morris that went to the fine leg boundary.
His 45-ball mayhem finally ended when he gave Jadeja the charge having hit the previous delivery deep into the cow-corner stand for his second six. The ball skidded through him and Mahendra Singh Dhoni completed an easy stumping.
Such was Finch's dominance that the normally aggressive Uthappa remained content in taking the singles and giving bulk of the strike to the Aussie opener.
Finch's dismissal certainly disturbed the momentum as Uthappa was holed in the deep of Morris' bowling. The likes of stand-in skipper Ross Taylor, Mitchell Marsh also failed with the bat to undo the good start provided by Finch.