Sri Lanka reached stumps at 275 for nine, after a stubborn fightback from opener Dimuth Karunaratne, who made 79, and former captain Angelo Mathews (83) rescued the touring side from early trouble.
The duo combined for a fourth-wicket stand of 133 after seamer Southee had reduced the visitors to nine for three inside the first four overs.
Niroshan Dickwella remained unbeaten on 73 to further thwart New Zealand's attack in the final session.
The 30-year-old Southee had spoken on Thursday of liking the look of a green pitch in Wellington after low, slow and spin friendly pitches in the United Arab Emirates in his team's 2-1 series victory against Pakistan.
He had also mentioned, however, that looks could be deceiving and while a green pitch might help initially, the Basin Reserve wicket tends to flatten out and become easier for batsmen to score later on.
After Kane Williamson won the toss and chose to bowl, Southee wasted no time in proving his worth on a humid, but fine day.
He trapped Danushka Gunathilaka in front for one on the final ball of his first over, had Dhananjaya de Silva caught by wicketkeeper BJ Watling for one before Kusal Mendis (two) flicked a delivery to Ajaz Patel at midwicket.
Karunaratne, who was caught off a no-ball from Colin de Grandhomme on 33, defied the initial onslaught and went on to bring up his 21st test half century, while Mathews scored his 33rd to resurrect their innings.
Wicketkeeper Dickwella then attacked New Zealand's bowlers, whose lengths shortened as the day progressed, with inventive scoops, flicks and aggressive shots behind square to produce an entertaining 10th test half century.
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
