RR defeated MI thanks to a dominant bowling performance by Sandeep Sharma (5/18) and a brilliant century from Yashasvi Jaiswal (104*).
Chahal became the first bowler to take 200 wickets in IPL history during the match.
Despite a fightback from Tilak Varma (65 runs) and Nehal Wadhera (49 runs), MI were restricted to 179/9.
Sandeep Sharma's fifer and early wickets from Trent Boult restricted MI's batting.
Jaiswal and Jos Buttler (35 runs) provided a strong opening stand (74 runs). Sanju Samson (38* runs) supported Jaiswal in a match-winning partnership.
Mohammad Nabi faced heavy hitting from RR batsmen, contributing to their rapid progress in the chase.
Jos Buttler (RR) and Nuwan Thushara (MI) were the Impact Player substitutes.