Jaiswal scored an unbeaten 104 off 60 balls, including nine boundaries and seven sixes, to lead Rajasthan to 1-183 after Mumbai struggled to 9-179 in their 20 overs.
Medium-pacer Sandeep Sharma collected 5-18 in four overs for Rajasthan while leg-spinner Yuzvendra Chahal took 1-48 - but in the process became the first bowler to reach 200 IPL wickets.
Jaiswal's previous highest score this season was 39.
He and opening partner Jos Buttler combined for 61 in the power play when rain interrupted the chase for 45 minutes without losing any overs.
Jaiswal didn't lose focus but Buttler was bowled in the eighth over for 50 off 31 balls.
Jaiswal accelerated, scoring his next 54 runs off 29 balls, including five more sixes.
In the process Jaiswal added 109 runs off 65 balls for the second wicket with skipper Sanju Samson, who finished unbeaten on 38.
The — IndianPremierLeague (@IPL) @rajasthanroyals sign off from Jaipur in style with plenty to celebrate 💗🥳Scorecard ▶� https://t.co/Mb1gd0UfgA#TATAIPL | #RRvMI pic.twitter.com/kW9mOqYNfUApril 22, 2024
At 22, Jaiswal became the youngest batter in IPL history to score multiple hundreds. His first was also against Mumbai, in last year's competition.
Put into bat after losing the toss, Mumbai suffered another top-order collapse against the Rajasthan pacers.
New Zealander Trent Boult got rid of Rohit Sharma for six, and Sandeep Sharma had Ishan Kishan caught behind for a three-ball duck.
Sandeep then sent back Suryakumar Yadav for 10 - leaving Mumbai shellshocked at 3-20 after 19 balls.
Chahal's milestone wicket, in his 153rd IPL game, was that of Mohammad Nabi (23).
Tilak Varma countered with a half-century off 38 balls, and finished with a team-high 65 for the Indians.
Nehal Wadhera added 49 off 24 deliveries - including four sixes - as the pair's partnership made the five-time champions competitive.
But Rajasthan won with eight balls to spare to stay top of the table after their seventh win in eight games. Mumbai are second to last.
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