Mumbai Indian shot to the top of the points table, courtesy their fifth win in six matches.
Skipper Glenn Maxwell, on his part played a typically breezy innings smashing 40 off 18 balls with the help of four boundaries and three sixes.
Earlier, the hosts were off to a steady start with Amla (104 not out) and Shaun Marsh (26) putting on 46 runs before Maxwell took just one over from pacer Mitchell McClenaghan, milking 28 runs, to change the complexion of their innings.
Rana finished unbeaten on 62, which came off 34 balls with seven sixes struck, while Hardik Pandya made an impressive cameo as he struck 15 off four balls as Mumbai won on 199-2 with 27 balls remaining. His 95-run knock against the good bowling attack of Sunrisers Hyderabad will boost his confidence when he plays against the Mumbai Indians on Thursday. He was out for 37 off 18 balls at 81-1. However, Mumbai bowling coach Shane Bond is not at all intimidated by the fact that KXIP are formidable at the Holkar Stadium.
Kings XI Punjab, who had a rather dismal season a year ago, started off strong, winning both matches at home.More news: Secret Service limits sidewalk access south of White House
Amla, on the other hand, took full advantage of the life he got on 3, when he was dropped off a hard chance by Rana, to first get to a superb half century in just 34 balls.
Captain Glenn Maxwell's recent form adds to the misery as others except for Hasim Amla and Manan Vohra have misfired so far.
Parthiv Patel fell off the penultimate ball of the powerplay, but Jos Buttler rallied on, building on their highest powerplay score and catapulting Mumbai to 100 in mere 7.5 overs, a record high again. MI is now third in the table, locked on 8 points with SRH and the leaders KKR, separated by net run rate. His ability to combine single with boundaries and sixes and also maintaining a certain calmness, despite pressure, is what makes him "a player to watch out for". Against Malinga alone, Amla smashed 51 runs in just 16 balls. Meanwhile, Buttler's maiden IPL fifty came up in the ninth over, off just 24 deliveries.
The Mumbai top order was on-fire in pursuit with Parthiv Patel and England worldwide Joss Buttler providing the early impetus before the former departed at 80-1 after just six overs having hit four fours and two sixes.
The IPL continues with Kolkata Knight Riders versus Gujarat Lions on Friday, live on Sky Sports 2 from 3pm.