RR registered their sixth win in 12 games to move one rung up to fifth in the 2018 IPL standings on Sunday.
RR beat MI to bring Rohit Sharma's men one rung down to sixth.
Earlier in the day, second-placed CSK beat table-toppers SRH but the result didn't affect the positions of either team.
Here is how all eight teams are placed on the table after Matchday 37.
TEAM M W L T P NRR
SRH 12 9 3 0 18 0.400
CSK 12 8 4 0 16 0.383
KXIP 11 6 5 0 12 -0.056
KKR 12 6 6 0 12 -0.189
RR 12 6 6 0 12 -0.347
MI 12 5 7 0 10 0.405
RCB 11 4 7 0 8 -0.261
DD 12 3 9 0 6 -0.478
Talking about the first game of the day, Ambati Rayudu scored his maiden IPL century as CSK made light work of table-toppers SRH in Pune.
Chasing 180 to win, Rayudu (100* off 62 balls) and Shane Watson (57 off 35 balls) added 134 runs for the opening stand in 13.3 overs to kill it as CSK won their eighth game in 12 matches. It was SRH's third defeat in 12 matches.
After a few quiet previous outings, Rayudu on Sunday played like a champion and totally destroyed the much-fancied SRH bowling. None of the SRH bowlers - with the exception of Rashid Khan - could contain Rayudu and Watson and only halfway through their defence, the visitors found themselves out the contest.
Watson and Suresh Raina (2) departed in quick succession and that was as good as it got for SRH because after that Rayudu - fourth man this season to score a ton - and MS Dhoni (20 not out) batted with great conviction to take CSK over the line in 19 overs with eight wickets in hand.
In the second match of the day, Jos Buttler smashed a 53-ball 94* to take RR to a comfortable win and keep their playoff hopes alive in Mumbai.
The England player's knock did CSK a big favour as RR's win confirmed a play-off berth for Dhoni's men.
During the course of his innings against MI, Buttler also equalled Virender's Sehwag record for most consecutive fifties (5).
With RR in pursuit of 169, Buttler batted with great control and reached the milestone with a four off Hardik Pandya in the 12th over. He took 35 balls to reach his fifty. He didn't just stop there and stayed till the end to ensure RR stayed in the hunt.
RR lost D'Arcy Short early but after that Buttler added 95 and 61 with Ajinkya Rahane and Sanju Samson respectively as the visitors took the contest in 18 overs. It was Mumbai's seventh defeat in 12 games and they were very much out of the reckoning.