Rayudu, who had played only once before this game against Rising Pune Supergiant where he was stretchered out with a groin injury, starred for the visitors with a 37-ball 63. His innings was laced with six fours and three sixes.
Tiwary (52 of 43 balls), playing his first game of the season, stitched together a 61-run stand with Rayudu for the third wicket before being involved in another 57-run association with skipper Rohit Sharma (27 of 21 balls).
Hardik Pandya (not out 1) and Krunal Pandya (not out 0) were at the crease at the end of the innings.
Trent Boult in his first spell returned splendid figures of 2-0-8-1, picking the prized wicket of Lendl Simmons who went back to the hut for a golden duck. The New Zealand pacer was pick of the bowlers returning figures of 2/30. Ankit Rajpoot bowled well too conceding just 14 runs in his three overs and also taking one wicket.
Boult, playing his fifth match this season, made the most of the 22-yard Eden strip which looked to have some bite for the quicks after the rain.
With Rohit at the crease and his enviable record at the venue in mind, Gambhir threw the ball to Sunil Narine in the fourth over. Narine has conceded just 77 runs in 71 balls to Rohit, also dismissing the India limited overs opener once in three innings at the Eden.
After six overs, the visitors were 51/1.
Just when Rohit looked good for another big innings at his favourite ground, Rajpoot put a spanner in the works with a cutter which the skipper tried to glance past short third man but was LBW.
Rayudu made the most of a reprieve in the 12th over when a Narine delivery spun back sharply to take a thin edge off the bat only for wicketkeeper Robin Uthappa to drop the catch.
The pair guided Mumbai to 100 runs in 13.1 overs before Tiwary was run out.
With Kieron Pollard at the crease, it was not such a big blow for Mumbai who had to up the ante. Rayudu smacked Kuldeep Yadav for a four and six before the chinaman bowler floated the ball wide to force the batsman playing after 37 days to come out of his crease and reach for the ball, handing Uthappa an easy stumping.
Pollard (13) could not do much damage toe-ending a Boult delivery for Yusuf Pathan to catch at cover.
KKR made just one change, replacing Chris Woakes who is nursing an ankle niggle with Boult while already-qualified Mumbai Indians made six changes to their side resting some of the first team players.
Krunal Pandya, R Vinay Kumar, Rayudu, Mitchell Johnson, Tim Southee, and Tiwary were all slotted in with Jasprit, Harbhajan Singh, Nitish Rana, Parthiv Patel, Mitchell McClenaghan, and Lasith Malinga making way.
Top 10 Batsmen with most Sixes in IPL 2017
Big hits of IPL-10
2 bookies arrested during IPL final, 77 mobiles recovered
David Warner wins IPL 2017 Orange Cap
Ben Stokes won the Most Valuable Player of IPL 2017 Award
IPL 2017: Special Awards
Disappointed to lose in the final says Smith
Kieran Pollard hails Mumbai team's character after IPL triumph
Mumbai Indians won by 1 run to clinch the IPL-10 title (Full Scorecard)
Mumbai beat Pune to win IPL