In a match reduced to 11-overs-a-side, Rajasthan plundered 3 for 150 and cruised to a 27-run win after Mumbai won the toss and elected to field.
Jaiswal hit an unbeaten 77 off 32 balls, with 10 fours and four sixes, and 15-year-old Sooryavanshi made a 14-ball 39, including a first-ball six over mid-on off premier fast bowler Jasprit Bumrah.
Earlier, it looked as if the much-anticipated clash between Sooryavanshi and Bumrah might not happen as the the Super Soppers struggled to clear the heavy rain. The match eventually started more than two hours late.
Mumbai's chase was dashed inside the 20-ball power play when Ryan Rickelton, Suryakumar Yadav and Rohit Sharma all fell for single-digit scores against Rajasthan pace. The former champions eventually finished on 9-123.
Mumbai lost the top three for just 22 runs and then further slipped to 5-46 when impact substitute leg-spinner Ravi Bishnoi (2-25) bagged the wickets of Hardik Pandya and Tilak Varma in his first over.
Mumbai's impact substitute Sherfane Rutherford and Naman Dhir played cameos of 25 runs each, but Rajasthan did enough damage up front through Jofra Archer (1-17), Nandre Burger (2-21) and Sandeep Sharma (2-26) to seal their third straight win.
Rajasthan top the table with three straight wins while Mumbai remain in the bottom half of the table with two points.
Earlier, Jaiswal gave Rajasthan a rollicking start with a 22-run first over as the left-hander smacked Deepak Chahar for four boundaries and a pulled six over mid-wicket.
Sooryavanshi didn't appear overawed while facing Bumrah for the first time in competitive cricket and lofted the world's best pace bowler for a straight six. Two balls later he picked up a slower ball for another six over square leg.
Jaiswal ensured Rajasthan got to well over-par score with another 22-run over against Trent Boult as he smashed back-to-back sixes while Sooryavanshi deposited the left-arm New Zealand fast bowler's shortish delivery to deep backward square leg for the maximum as Rajasthan raced to 58 off three overs.
Pandya (0-17) stemmed the flow of runs with a four-run fourth over before Shardul Thakur brought an end to an entertaining 80-run opening stand off just 30 balls. Sooryavanshi was distraught when he holed out to deep cover as Varma jumped high and grabbed a good catch over his head.
Afghanistan spinner AM Ghazanfar (2-21) and Bumrah (0-32) tried to limit the damage but Jaiswal raised his half-century off 23 balls and then hit three boundaries in Thakur's last over to give Rajasthan an imposing total.
