Travis Head's rapid hundred trumped Rachin Ravindra's gallant 116 as Australia survived late drama against New Zealand before winning the highest-scoring match in World Cup history by five runs to close in on a semifinal spot on Saturday.

Head smashed 109 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.

Ravindra led New Zealand's spirited reply with his second hundred of the tournament and Daryl Mitchell made 54 to keep the 2019 runners-up in the hunt.

Australia regained control after Ravindra fell in the 41st over but James Neesham injected fresh drama into the contest with a never-say-die 58 even though New Zealand ended just short of their target on 383-9.

"That was awesome," Australia captain Pat Cummins said after their fourth win in six matches.

"Sometimes I have to remember I'm out in the field, not a spectator. A fantastic game, they kept coming at us."

Head had missed Australia's first five matches with a fractured hand and he looked determined to make up for the lost time, racing to a 25-ball fifty as he and Warner took Australia to the 150-mark in the 15th over.

Glenn Phillips broke the burgeoning stand by taking a return catch to dismiss Warner, but Head raced to a 59-ball century.

Phillips came to New Zealand's rescue again breaching Head's defence with a skidding delivery to end the batter's 67-ball blitz, which was studded with seven sixes and 10 fours.

Glenn Maxwell (41) and Josh Inglis (38) produced breezy cameos and skipper Pat Cummins clobbered four sixes in his 37 off 14 balls before Australia collapsed with four balls left in their innings.

Devon Conway (28) and Will Young (32) gave New Zealand a rapid start but Josh Hazlewood removed both in successive overs to peg them back.

Ravindra and Mitchell steadied the innings playing sensible cricket.

Ravindra brought up his 77-ball hundred with a six off Maxwell and it was because of his stellar knock that New Zealand entered the final 10 overs of their innings confident of scoring the required 97 runs for victory.

Cummins removed Ravindra in the 42nd over but Neesham produced a belligerent 58 to keep the contest alive.

New Zealand needed 19 off the final over from Starc, who conceded a single off the first delivery before bowling a wide down the leg side which ran to the boundary.

Needing 13 off five balls, Neesham squeezed six runs of the next three deliveries before being run out.

That left Ferguson with the job of hitting the final delivery for six, but he drilled it straight to the cover fielder instead.

"It was a fantastic game of cricket," New Zealand captain Tom Latham said.

"There were ebbs and flows throughout the 100 overs. Obviously to get so close hurts."