Australia's batsmen went through the campaign without scoring a century, the first time this has happened at home in a series of four or more Tests since 1882-83.
It came after India also amassed a 292-run first-innings lead in Melbourne last week, only on that occasion they opted to bat again themselves in the 137-run flogging. Mohammed Shami (2-58) bowled Pat Cummins (25) with a ball that kept low on the sixth ball after resumption of play.
Peter Handscomb (37) was the next to have his castle toppled, catching an inside edge from Jasprit Bumrah's bowling, which careened into his pads and then the stumps.
Kuldeep (5-99) then trapped Nathan Lyon for no score.
Kuldeep, playing his first match in the series, picked up his second five-wicket haul in Test cricket, with his first coming against the West Indies at Rajkot in October of previous year.
Mitchell Starc and Josh Hazlewood, who was dropped on zero, combined for a final-wicket stand of 42 that spanned 14 overs but only delayed the inevitable.
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The inclement weather didn't relent until lunchtime and the morning session was completely washed out.
India denied Australia any real possibility of a victory here by batting for almost two full days with Cheteshwar Pujara (193) and Rishabh Pant (159 not out) scoring hundreds.
Australia, rolled for 300 in their first dig, reached 6-0 in their second innings on Sunday when bad light prompted an early tea break and ruined any hope of further play.
For India, apart from Yadav, Mohammed Shami and Ravindra Jadeja took two wickets each. Starc finished on 29 not out.
Torrential downpour in Sydney spared Australia's blushes on Day 3 of the New Year's Test, as India extended their dominance to stay on course for a thumping victory in the series finale.
Australia 2nd Innings: Usman Khawaja batting 4; Marcus Harris batting 2.