Finch scored an attractive 42-ball 65 with the help of eight fours and two sixes while Yuvraj hit an impressive 24-ball 34, laced with two fours and three sixes.
Luke Wright helped the visitors finish with flourish, courtesy his breezy 34 off 10, during which he found the fence six times.
Opener Robin Uthappa also scored a useful 37 off 33 deliveries with the help of four fours and added 83 runs for the opening wicket stand with Finch after being invited to bat by KXIP skipper Adam Gilchrist.
Finch led from the front after being dropped by Gilchrist off Mahmood in the second over of the innings.
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Both Finch and Uthappa gave the visitors a flying start as they took the side to 77 in first ten overs. The hosts' bowlers appeared clueless as the duo helped Pune cross 50-mark in just six overs.
Parvinder Awana gave Punjab their first breakthrough by dismissing Uthappa, who was caught by Gilchrist behind the wickets in the 11th over.
Next man-in, Yuvraj Singh made his intentions clear from the outset as he smashed leg-spinner Piyush Chawla for a six and a four in the 14th over.