New Zealand has completed a one-sided demolition of South Africa, winning the first Test by an innings and 276 runs before lunch on day three day to end a winless run that lasted almost 20 years.

Tim Southee took five wickets as New Zealand bowled out South Africa for 111 in their second innings, a paltry total that was actually better than their first-innings haul.

The result ended a 16-match winless streak by New Zealand in Tests between the two nations, dating back to March 2004.

The Black Caps have never won a series against South Africa but look likely to break their duck, barring a major turnaround in the second Test of the two-match series in Christchurch.

"It's a special victory," Southee said.

"It was a clinical three days from everyone. Different guys stepped up at different times. It's the way we want to play and have played for NZ for a long time now."

Resuming at 3-34 in their second innings at Hagley Oval, South Africa lost their remaining seven wickets in only two-and-a-half hours, their batters having no answer to New Zealand's relentless pace attack.

Southee bowled with his usual precision, taking 5-35, while player of the match Matt Henry picked up 2-32 to add to the seven wickets he collected in the first innings.

He also made 58 not out batting at number 11.

Not a single South Africa batter made a half-century in the match, with Temba Bavuma's knock of 41 in the seconds innings the best of the bunch.

The second Test starts on Friday, leaving South Africa with nearly a week to regroup from their shocking performance.

There were mitigating circumstances, as they had to endure a 10-day lockdown on arrival, and also crucially lost the toss on a wicket that offered New Zealand's dangerous pace attack plenty of assistance on the first morning.

Still, the dominance of the reigning world Test champions suggests the visitors face an uphill task to claw back and draw the series.

ABC/wires