Put in to bat, the Sunrisers were reduced to 52 for five in the ninth over with IPL debutant Sandeep Sharma (3/21) doing most of the damage before Parthiv (61) anchored the visiting side's innings to post a defendable total.
Thisara Perera pushed Sunrisers to 150 with a quickfire 32 not out from just 19 balls as they added 94 runs in the second half of their innings after being reduced to 56 for five after 10 overs.
Parthiv hit five fours and two sixes in his 47-ball innings while Perera's knock had two fours and as many sixes.
The Sunrisers started well, with openers Shikhar Dhawan and Parthiv looking in good form.
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But, after Dhawan fell in the fifth over to Harmeet Singh, 19-year-old medium pacer Sandeep struck in his first over removing Hanuma Vihari (5) who perished while trying to cut an out-swinging delivery only to find a safe pair of hands of David Miller.
Darren Sammy also returned to the dressing room without opening account and the Sunrisers were 52 for five in the ninth over.
But, Parthiv held one end intact and with Karan Sharma stitched a crucial 42 runs for the sixth wicket.
Karan hit a 18-ball 22 before he edged a Parvinder Awana delivery into the safe hands of wicketkeeper and KXIP skipper Adam Gilchrist.