Making his debut for Mumbai Indians, Tiwary seized the opportunity with a glittering 43-ball 52 (9x4) while Rayudu who made a comeback after more than a month was Mumbai's top- scorer with a spectacular 63 from 37 balls (6x4, 3x6).
Ruled out after a groin injury in their first match in Pune, a fit-again Rayudu made full use of his reprieve by wicketkeeper Robin Uthappa on 10 to notch up a half-century in 32 balls.
But Rayudu ensured that they keep the run-rate ticking with his counter-attacking innings against the KKR pacers who started off well after they opted to bowl.
Rayudu hit Kuldeep Yadav for successive boundary and a six before being brilliantly stumped in the penultimate over.
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KKR bowling once again faltered at the death and conceded 55 runs in the last five overs.
Kiwi pacer Boult fired in a superb first over and made the ball do the talking with excellent swing and bounce. Not only Boult troubled Tiwary but Windies explosive batsman Lendl Simmons looked clueless and survived a big appeal in an over where he conceded just two runs.
The pitch looked to have some fizz and Boult made full use of it. He finally got the reward in Simmons in his next over. Simmons had a testing time and failed to open his account from five balls.
Sharma took the attack on to KKR camp especially against India pacer Umesh Yadav, smashing him for two exquisite boundaries and a six in his next over in an effortless display.
Tiwary, who played for Rising Pune Supergiant last season, complemented well as he along with Sharma put on 50 runs in 30 balls.
The duo looked in good touch but Gambhir's move to bring in unheralded Ankit Rajpoot did the trick as the bowler trapped Sharma in the second ball to break the partnership.
Earlier the match began after a 30-minute delay as rain accompanied by thunderstorm lashed the city for more than half an hour around 4pm.