Sharma also became the fastest to score 2,000 ODI runs against Australia.
Shikhar Dhawan smashed 117, his 17th ODI century, and forged two significant partnerships with fellow opener Rohit Sharma and skipper Virat Kohli to power India to a commanding 352-5.
In contrast, several frontline Australia batsmen got decent starts but none could bat deep enough as the five-time world champions, all out for 316 in exactly 50 overs, tasted their first defeat in the tournament.
Earlier, Kohli opted to bat on a used wicket at the Oval but the flying start he may desired did not materialise.
Australian quicks Mitchell Starc and Pat Cummins ensured the first five overs yielded just one boundary and a half chance.
Rohit, then on four, got lucky as his chip burst through an airborne Nathan Coulter-Nile's fingers at short mid-wicket.
India managed only 41 runs in the first 10 overs but Rohit and Dhawan were content to weather the hostile period before chancing their arms against other bowlers.
Dhawan welcomed Coulter-Nile with three boundaries in his first over and Rohit hooked the quick for a six in his fourth.
Coulter-Nile returned to end the burgeoning 127-run stand by dismissing the opener for 57.
An unperturbed Dhawan went on to raise 93 runs with Kohli (82) to lay the foundation for a big total in front of a crowd of predominantly Indian fans who turned the stands into a sea of blue.
The left-hander brought up his third ODI century at the Oval in five innings, underlining his fondness for English conditions having finished as top scorer at the Champions Trophy here in 2013 and 2017.
Starc eventually dismissed Dhawan but Kohli and a promoted Hardik Pandya (48), who smacked three sixes in his 27-ball blitz, provided the late flourish to help India past the 350-mark.
Australia seemed to have luck on their side when Aaron Finch's men embarked on what could have been the highest successful chase in a World Cup match.
David Warner dragged a Jasprit Bumrah (3-61) delivery onto the leg stump but the zing bail, for the fifth time in the tournament, did not fall off the groove despite the contact.
Finch departed for 36 chasing a non-existent second run but Warner (56) then collaborated with Steve Smith in a 72-run stand, although he looked subdued as he brought up his second fifty in three matches.
Usman Khawaja made 42 but Australia suffered a body blow when Smith was out leg-before for 69 after India decided to review the original not-out decision.
Australia's narrow victory against West Indies was secured with Coulter-Nile's belligerent 92 at number eight but he could not repeat that performance.
Alex Carey, who had dropped Pandya on nought, made 55 not out but could not change the outcome of the match.