Five-time champions Australia edged out gallant New Zealand by just five runs in the highest-scoring World Cup game in history on Saturday.

Australia piled up 388 all out as Travis Head top scored with 109 and fellow opener David Warner made 81.

New Zealand battled hard with Rachin Ravindra making 116, Daryl Mitchell adding 54 and Jimmy Neesham supplying late fireworks with a 33-ball fifty before they finished on 383-9 in 50 overs.

With a total of 771 runs, it was the highest scoring game at a World Cup, beating the 754 scored in South Africa's win against Sri Lanka earlier in the tournament.

"That was awesome. Sometimes I have to remember I'm out in the field, not a spectator. A fantastic game, they kept coming at us," said Australia skipper Pat Cummins.

In a dramatic final over played out in the shadow of the Himalayas, New Zealand needed 19 to win.

Trent Boult scampered for a single before Mitchell Starc donated five wides.

Neesham, one of the stars of the 2019 final which New Zealand lost to England, then took six runs off the next three balls.

However, attempting another two, he was run out from a fine throw by Marnus Labuschagne from the fence.

That left Lockie Ferguson, who had injured his Achilles in the field, needing to perform the heroics off the last ball.

Starc fired the ball in on a full length and Ferguson could only push it to the covers, leaving the Kiwis heartbroken.

"It was a fantastic game of cricket. There were ebbs and flows throughout the 100 overs," said New Zealand captain Tom Latham.

"To get so close hurts. It was a fantastic game."

The result left both sides with four wins and two defeats each and well-placed for the semi-finals.

Earlier, Head, playing his first match of the tournament after being sidelined with a broken hand, reached his fourth one-day international hundred off 59 balls with 10 fours and six sixes.

The 29-year-old had brought up his 50 off 28 balls and then made the most of being dropped on 70 and 75.

He was eventually clean-bowled by off-spinner Glenn Phillips with Australia reaching 206-2 at the halfway stage.

With Warner, Head had put on 175 in the first 20 overs before his veteran partner was dismissed.

Warner, who turned 37 on Friday, had been looking for a third successive century but eventually fell for 81 when he chipped a catch back to Phillips.

Phillips then accounted for Steve Smith (18) as he claimed career-best figures of 3-37 before fellow spinner Mitchell Santner got in on the act.

Santner beat the defences of Mitchell Marsh (36) and the left-armer then dismissed Labuschagne (18) after the batsman had been dropped on one.

Neesham had middle-order dangerman Glenn Maxwell caught at long-off by Trent Boult for a 24-ball 41.

Maxwell had come into the match fresh from a World Cup record 40-ball hundred against the Netherlands.

Josh Inglis raced to a 28-ball 38, putting on 62 for the seventh wicket with skipper Pat Cummins (37).

In reply, New Zealand, runners-up in the last two World Cups, saw Will Young (32) and Devon Conway (28) put on 61 for the first wicket before both fell to Josh Hazlewood.

Mitchell hit his third fifty of the tournament to follow his 130 last time out against India but fell on 54 when leg-spinner Adam Zampa had him holing out to long-on with his team on 168-3 after 24 overs.

Mitchell put on 96 for the third wicket with Ravindra.

The 23-year-old Ravindra, who scored 123 in the opening win over England, reached three figures from 77 balls with seven fours and five sixes.

But with New Zealand needing 97 to win off 60 balls, Ravindra was caught in the deep off Australian skipper Pat Cummins for a fine 116.

That left the Kiwis on 293-6 but they battled hard to take the game to the final over thriller.