The South African cricketers have taken an unbeatable 2-0 lead in the one-day series, thrashing New Zealand by 72 runs in the second match at Mount Maunganui.
After restricting the Proteas to 282 for nine, with the opening batsman Hashim Amla leading the scoring for the tourists with a century, the Black Caps again struggled badly with the bat.
A half century to wicketkeeper Luke Ronchi in a 10th-wicket record partnership of 76 with bowler Mitchell McClenaghan offered some resistance, but the wicketkeeper was the last wicket to fall for 79, and the hosts were bowled out for 210 in the 47th over.
McClenaghan was not out for 34 - his highest score, and the second-highest score for the day for the New Zealand side: the tail-ender's efforts impressive but another indicator that all is not well with his team's batting.
They won the toss and chose to bowl first on a beautiful day at Bay Oval, but got little reward as Amla led the scoring with a classy century, before Southee cleaned him out for 119, with the tourists 257 for four in the 45th over.
Amla was the first of five wickets to fall for just 26 runs. Southee, Mitchell McClenaghan, Trent Boult and Corey Anderson grabbed two wickets each.
The Black Caps made two changes to their playing XI with paceman Tim Southee returning to spearhead the bowling attack alongside fellow seamer Mitchell McClenaghan.
Pacemen Kyle Mills and batsman Matt Henry were left out.