Southee finished with four for 97 off 25 overs in Australia's second innings of 385-7 declared.
Two of his deliveries would have had the eyes of Australia's seamers, Mitchell Johnson, Mitchell Starc and Josh Hazlewood, lighting up. They landed beside a substantial crack and jagged sharply away to the offside, easily beating the defensive shot of batsman Peter Nevill.
Another ball from Trent Boult shot along barely above the ground, at lefthander Johnson.
But in the 37 minutes, there were no alarms for the New Zealand batsmen. Latham looked impressive and Guptill was safe enough, albeit getting a couple of fours airily through the backward point area.
The threat of Mitchell Starc had been seen off - his three overs had been despatched for 27.
Johnson had time to bowl just 1.2 overs in his last hurrah. It was a damp squib, in more ways than one, for the champion quick bowler who saluted the crowd as he left test cricket, probably for the last time.
New Zealand's bowlers had a poor match in Brisbane and a bad opening day in Perth as Australia rattled up 416-2.
But since then the seamers have picked up their game. Southee has been good, Doug Bracewell has had solid periods and Trent Boult, although still well short of his best, has had his moments.
Australia, looking to get thing going in the first session today with a declaration in mind, were set back early by the loss of fast-scoring captain Steve Smith in the fifth over of the day, and dawdled along for a while. The first hour produced just 21 runs and two wickets.
Bracewell was particularly effective early on. It wasn't until Johnson, arriving to a guard of honour by the New Zealanders and a standing ovation in the stands, clunked some quick runs before lunch that things got moving.
When Australia declared 56 minutes after lunch, New Zealand had about 48 overs to bat, and a steep run rate of 6.7 to pursue.
The pitch had been giving some cause for concern earlier in the day, and late on the fourth afternoon. Then again, that's what should be expected. Bowlers should find conditions turning their way.
And in the case of this test, it's been a treat for the batsmen, who have rattled up six centuries - three in each of the first three innings - so the bowlers deserved some late help.