India launched their home World Cup campaign with a six-wicket victory over Australia after Virat Kohli and KL Rahul guided them through a jittery run chase on Sunday.

The hosts probably expected their chase to be a cakewalk after their spin-heavy attack bundled out the five-time champions for 199 with three deliveries left in the Australian innings.

India, however, made a shocking start to their reply with three of their top four batters falling for ducks -- for the first time in an ODI -- inside two overs.

Dropped on 12 by Mitchell Marsh off Josh Hazlewood, Kohli went on to make 85 as he masterminded yet another successful chase for India.

His partner in the 165-run fourth-wicket stand, KL Rahul, produced a chanceless knock of 97 not out as India reached the target in 41.2 overs.

Australia would be particularly unhappy with their batting as no one reached fifty though David Warner (41) and Steve Smith (46) got decent starts after Pat Cummins elected to bat.

Kohli took a sharp, diving catch in the slip to dismiss Marsh for a duck when the opener edged Jasprit Bumrah in the third over.

Warner and Smith combined in a rebuilding job though boundaries were not easy to come by as India's three-pronged spin attack applied the chokehold.

India had used Kuldeep Yadav sparingly in the buildup to the tournament wary of over-exposing him and the wrist-spinner struck two crucial blows.

Kuldeep broke the 69-run stand when he took a return catch to dismiss Warner before Jadeja (3-28) wrecked Australia's middle order.

The left-arm spinner pegged back Smith's off-stump, removed Marnus Labuschagne caught behind and trapped Alex Carey lbw to leave Australia reeling.

Kuldeep returned to remove Glenn Maxwell and Ravichandran Ashwin sent back Cameron Green to reduce Australia to 140-7.

Cummins hit their first six of the match in the 40th over but it was Mitchell Starc's 28-run cameo down the order that took them near the 200-mark.

Defending a paltry total, Australia's pace attack decided to fight fire with fire and Starc set the tone by removing Ishan Kishan for a first-ball duck.

India's poor start became a veritable nightmare as Josh Hazlewood began with a double-wicket maiden.

Hazlewood trapped Rohit lbw with his third ball and Shreyas Iyer became the third Indian to fall for a duck when he slapped the ball to Warner at short cover.

It could easily have been 20-4 for India had Marsh not dropped Kohli in what proved a costly mistake.

While Kohli absorbed pressure at one end, Rahul released it by hitting Adam Zampa for three boundaries in one over as the batters focused on risk-free accumulation of runs.

Kohli fell to Hazlewood but Rahul held firm to seal India's victory with his second six.