Travis Head's return to action proved worth the wait for Australia as the opener smashed a blazing hundred in his World Cup debut to set up a five-run victory in a high-scoring thriller against New Zealand on Saturday.

The left-hander missed Australia's first five matches in the tournament with a broken hand that delayed his arrival in India for the showpiece event.

He made up for lost time with a 59-ball century and forged a breakneck 175-run opening stand with David Warner to set Australia on their way to an imposing total of 388.

The impact of his return could be gauged from the fact that Australia plundered 118 in the best Powerplay of the tournament so far.

"Nice to be back, it was very close in the end, a hell of a game," Head said after collecting the player-of-the-match award for his 109 off 67 balls, including seven sixes and 10 fours.

"I've only had a couple of hits, a bit like the World Test Championship where I was off for six or seven weeks," he said of his buildup for the World Cup.

Mitchell Marsh dropped down to number three to clear the opener's slot for the returning Head, who slotted back in at the top effortlessly.

"We play together really, really well, we combine really well," he said of his collaboration with fellow left-hander Warner.

"Play what comes towards us, try and play positive and do what we can."

The 29-year-old Head was ruthless but did give away some chances that New Zealand failed to capitalise on as they were unusually sloppy in the field.

He got a friendly welcome too with Matt Henry bowling back-to-back no-balls in the third over of the day. Head smashed both of the resulting free-hit deliveries for six.

Head raced to a 25-ball fifty and got a couple of reprieves afterwards en route to a blistering hundred.

Mitchell Santner floored a return catch when the batter was on 70 and Glenn Phillips grassed an easier catch at mid-wicket off Rachin Ravindra when on 76.

Glenn Phillips eventually got the better of him when the part-time spinner disturbed Head's stumps with a skidding delivery.

Five-time champions Australia are currently fourth in the points table following their fourth win in six matches, level with New Zealand on eight points but behind on their net run-rate count.