Rana, who hit an unbeaten 48, anchored the 153-run chase on a slow-paced Wankhede wicket to help KKR beat RR by seven wickets on Monday and snap their five-match losing streak.
Kolkata Knight Riders defeated in-form Rajasthan Royals by seven wickets to snap their five-match losing streak in the Indian Premier League.
It was the 17th over when Chahal removed Venkatesh Iyer off his first delivery and then Shreyas, Shivam Mavi and Pat Cummins off the fourth, fifth and sixth balls to completely turn the match.
Put in to bat, Rajasthan Royal rode on Buttler's 61-ball 103 innings, which was studded with nine boundaries and five maximums.
Royals made three changes, bringing in fast bowlers Obed McCoy and Trent Boult alongside Indian batter Karun Nair and for KKR, pacer Shivam Mavi was picked in place of Aman Khan.
KKR have virtually assured themselves of a play-offs berth in the IPL after their 86-run win over Rajasthan Royals on Thursday.
KKR had a mixed bag in the second leg of the tournament so far, winning four and losing two games.