Chasing 168 to win, Rajasthan were cruising along at one stage and it looked they would coast home when Sanju Samson (52) and Ben Stokes (40) were batting.
Royals were cruising along at 110/2, when Mumbai's star bowling pair of Jasprit Bumrah and Mustafizur Rahman wrecked havoc, picking up 4 wickets between them and conceding only 15 runs.
The fall of wickets put Mumbai on top but Gowtham and Jofra Archer kept their calm to pull things back, smashing Mustafizur and Bumrah for 15 & 18 runs respectively off the 18th and 19th over.
That left Hardik Pandya with just 10 runs to defend. He dismissed Archer off the first ball but then Gowtham hit the next one for a boundary and smashed another into the crowd much to the delight of Rajasthan fans.
Earlier, IPL debutant Jofra Archer showed exactly what Rajasthan had been missing all this while as he bowled superbly towards the death, ending with figures of 3/22 in his 4 overs to restrict Mumbai to 167.
Evin Lewis was dismissed for a golden duck but then Suryakumar Yadav - who has been showing good form - got together with Ishan Kishan to put up a 130-run partnership.
Both players scored fantastic half-centuries, scoring 72 & 58 respectively as it seemed Mumbai would score somewhere around 200.
But then Rohit Sharma was run out for 0 and Archer removed the Pandya brothers. Pollard's poor form with the bat didn't help either as he scored 21 off 20 balls. Archer was well supported by Dhawal Kulkarni who ended with figures of 2/32.
Archer was also named man-of-the-match for his sensational effort.
The win kept Rajasthan in touching distance of the top 4 spots as now they have 3 wins and 3 losses from 6 games.
Champions Mumbai meanwhile compounded their misery as they still have only 1 win to their name in 5 games. They will next face Hyderabad on Tuesday, while Rajasthan will enjoy a six-day rest before their next game.
First Published: April 23, 2018, 7:50 AM IST