CHENNAI, India (Reuters) -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-times champions for 199 with three deliveries left in the Australian innings.

India, however, made a shocking start to their reply with there 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 collaborator 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 in the low-scoring match though David Warner (41) and Steve Smith (46) got decent starts.

(Reporting by Amlan Chakraborty in New Delhi; editing by Ed Osmond)