DHARAMSALA, India (Reuters) -Travis Head's rapid hundred trumped Rachin Ravindra's gallant 116 as Australia beat New Zealand by five runs in the highest-scoring match in World Cup history to stay on course for a semi-final slot in the 50-overs tournament on Saturday.

Head smashed 109 off 67 balls in his first match of the World Cup and forged a breakneck 175-run opening stand with David Warner (81) to propel Australia to a commanding 388 all out at the Himachal Pradesh Cricket Association Stadium.

Glenn Maxwell (41), Josh Inglis (38) and skipper Pat Cummins (37) provided breezy cameos down the order before Australia were all out in 49.2 overs.

Ravindra led New Zealand's spirited reply with his second hundred of the tournament and Daryl Mitchell made 54 to steady their innings.

The 2019 runners-up looked out of the contest after Ravindra fell in the 41st over but James Neesham injected fresh drama with a never-say-die 58 but it was not enough in the end as New Zealand ended just short of their target on 383-9.

(Reporting by Amlan Chakraborty in New Delhi; Editing by Hugh Lawson)