Just as KXIP looked like they would chase down the stiff target in quick time, Karthik departed with R P Singh removing him in the first ball of his second spell and his last over.
R P Singh removed Marsh five balls later, caught and bowled to give a twist to the match. From 142 from two, KXIP were 145 for four in the space of an over.
KXIP needed 30 from four overs but David Hussey got able support from Mandeep Singh (15 not out from 10 balls) to chase down the target.
Earlier, captain Mahela Jayawardene led from the front with a classy 76 as KTK post 178 for seven.
Opening with Brendon McCullum (32), Jayawardene held the innings together with a responsible 52-ball knock which was studded with eight fours and two sixes in KTK's 'home' match.
KTK made a rollicking start after being put into bat, with openers Jayawardene and McCullum stitching 93 runs in just 8.4 overs on a batting-friendly pitch.
At the halfway stage, KTK were 103 for one and they looked like crossing 200 only to fritter away the superb start and ended less than 180.
In Image: Kochi Tuskers Kerala batsman and team captain Mahela Jayawardene plays a shot