Marsh who scored his runs in only 40 balls paced his innings nicely as Kings XI, chasing MI's competitive score of 163 for 6, reached the target with three balls to spare.
Kings XI needed 20 runs in the last two overs and Munaf Patel seemed to have swung the game a bit towards MI's way with his first four balls of the 19th over before the left-handed Marsh swung the fifth, a short one, over mid-wicket for a six.
The timely hit brought down the winning target to nine from the last over and off the first ball of the 20th over bowled by Thisara Perera, Marsh struck a six over point which proved to be a decisive blow.
In all, the Australian batsman hit five fours and three sixes and his innings provided the visitors with only their third victory in the season in seven games while dumping the home team to their fourth defeat in the same number of matches.
The second successive home defeat for MI kept their points tally to six while the victory brought Kings XI at par with them on points.
Earlier winning the toss and choosing to bat first, MI posted 163 for six courtesy a 51-ball-79 by James Franklin.
The lanky left-handed batsman opened the innings with the fit-again Sachin Tendulkar (23. Tendulkar played only his second game of the tournament after missing four in between, put on a half century stand for the first wicket and then added a quick-fire 75 runs in just 36 balls with Dinesh Karthik (35 in 20 balls) to pave the way for the competitive score.