Chasing a target of 199, MI reached in 15.3 overs with Buttler hitting 77 off 37 and Rana scoring an unbeaten 62 off 34 balls. Mumbai Indians now have 10 points from six games.
Earlier, opener Hashim Amla's unbeaten 60-ball 104 powered Kings XI Punjab to a formidable 198 for four being sent into bat.
Amla top-scored for Kings XI Punjab with his maiden T20 century, while skipper Glenn Maxwell smashed his way to 40 off just 18 balls, at the Holkar Cricket Stadium.
Kings XI Punjab were off to a good start with Amla adding 46 runs for the first wicket with Shaun Marsh (26).
But the partnership that really boosted KXIP's run rate was the one between Amla and Maxwell, the duo scoring 83 for the third wicket in 5.3 overs at a staggering rate of 15.09.
Amla struck eight fours and six sixes during his whirlwind knock.