Chasing a target of 189, India were 16/3 and subsequently 39/4 but Rahul held his nerves during a 91-ball knock that had seven fours and a six. He added 108 for the unbroken sixth wicket stand alongside Ravindra Jadeja (45 not out).
KL Rahul revelled under pressure with a composed 75 after Mohammed Shami's mesmerising spell of seam bowling as India overcame initial jitters with elan in their comfortable five-wicket win against Australia in the opening ODI in Mumbai on Friday. (More Cricket News)
India now lead the three-match series 1-0.
After being put in to bat, Australia suffered a dramatic collapse, losing six wickets for 19 runs inside eight overs to get bowled out for 188 in 35.4 overs, courtesy 3/17 from Shami.
Mitchell Starc then blew away the Indian top-order with some incisive swing bowling as India were left tottering at 39 for 4 just after the end of the powerplay.
Skipper Hardik Pandya (25) did stem the rot, but India weren't out of the woods when he was dismissed with the scoreboard reading 83 for 5.
But Ravindra Jadeja (45 not out, 69 balls), after having bowled nine tight overs of left-arm spin, gave adequate support in his unbroken 108-run stand with Rahul.
India won the game in 39.5 overs.
But Rahul does deserve the credit for anchoring the innings in the face of a storm, and has taken to the role of a No.5 keeper-batter like fish takes to water.
He enjoys the low-scoring scrappy battles and Friday at Wankhede was one such occasion.
The twilight hour, however, did belong to Starc. The Australian quick moved the new ball dangerously in the air as well as off the surface. He pinned Virat Kohli (4) in front of the wickets off the penultimate ball of the fifth over and, with the final delivery of that over, trapped Suryakumar Yadav leg-before for a first-ball duck.
The right-arm pacer Sean Abbott too got the ball to jag back in, trapping Shubman Gill leg-before, but the Indian batter reviewed successfully after being adjudged out.
Gill had luck riding in his favour as Australia missed two tough chances behind the wickets, but the Indian could not capitalise.
Starc bowled fuller deliveries outside off to get the Indians to drive, hoping to find edges or shots hit in the air.
Deployed on a longer six-over burst, Starc finally succeeded after Gill hit the left-armer for two fours. The bowler had him caught at point for 20 off 31 balls with four fours in all, leaving India in a precarious position at 39/4 in 10.2 overs.
This is when Rahul showed his experience as he didn't take undue risks, but, at the same time, punished the loose balls as and when necessary. He hit Adam Zampa into the deep mid-wicket stands. The key was rotation of strike as Rahul and Jadeja ran 56 singles between them.
But credit should be given to Pandya for marshalling the resources well on his ODI captaincy debut, albeit as a stand-in one.
The idea to bring in Shami for an early second spell proved to be a masterstroke as Australia from 169/4 just collapsed like a house of cards.
He got Josh Inglis to drag one back onto his stumps and then in his next over, the delivery to Cameron Green that sent the off-stump cartwheeling was a real peach.
It pitched on line of off-stump and Green had to commit, but there was a shade late movement that beat the batter and knocked back the off-stump.
The veteran pacer helped India pull things back after an attacking 65-ball 81 from Mitchell Marsh set Australia on the course for a competitive total, as his second spell of 3-2-8-3 broke the back of Australia's resistance after a sparkling start.
Shami finished with brilliant figures of 6-2-17-3.
On the other hand, Siraj, who provided an early wicket in the second over, also enjoyed success in his second spell to return with 5.4-1-29-3, snaffling the last two wickets in the Australian innings.
Marsh provided Australia with a rollicking start -- cracking 10 fours and five sixes in his first-ever innings as an opener in ODIs -- on his comeback to international cricket after a three-month layoff following an ankle surgery.
Marsh's charge in the first half of the game ensured Australia kept moving briskly towards a big total, but India kept making inroads at regular intervals and eventually bundled them out for a below-par score.