Brendon McCullum and Martin Guptill were made to survive a testing 12 overs before stumps but a rash shot from McCullum, two balls after he had hit a six, saw him depart for 13. Guptill and Kane Williamson eked out a lead of nine and closed the day on 35-1.
That New Zealand have a chance of winning just their second test of 2012 is largely due to Southee's first turn with the ball. He claimed four of the first five wickets to fall to reduce the hosts to 50-5, picking up where he left off in the whites.
In his side's last test against India in Bangalore, Southee recorded first innings figures of 7-64 - the sixth-best return by a New Zealand bowler. While India eventually prevailed, Southee set about repeating that effort in a devastating first spell at the Galle International Stadium.
After striking shortly before stumps on Sunday the 23-year-old claimed 3-17 while bowling in tandem with an equally dangerous Trent Boult, with the pair creating several other nervous moments for the Sri Lankan batsmen.
Southee's first wicket came on the fourth ball of the day, getting Tharanga Paranavitana to play on to reduce Sri Lanka to 9-2. With both openers gone for ducks the heat fell on the Sri Lankan middle order and, like their Kiwi counterparts yesterday, they failed to deal with the pressure.
Southee was getting significant swing in the humid conditions and he used it to terrorise Suraj Randiv, finding the outside edge on consecutive balls with identical out-swinging deliveries. The first edge flew straight to McCullum at third slip and, after he dropped a simple catch, Guptill snagged the second much to McCullum's relief.
Boult then chimed in with the prized wicket of Kumar Sangakkara, claiming the veteran batsman for five to add to an impressive list of career scalps already boasting Chris Gayle, Jacques Kallis and Sachin Tendulkar.
Southee struck Thilan Samaraweera on the pad to complete a fine first hour and make bowling advisor Chaminda Vaas appear an inspired hire but, just when the Black Caps were threatening to skittle Sri Lanka, Mahela Jayawardene and Angelo Mathews came together.
The pair batted safely through the middle session to both bring up their half centuries, particularly flourishing against the ineffective Doug Bracewell.
Shortly after tea, though, James Franklin took his first test wicket since 2009 to dismiss Mathews for 79 and end the sixth-wicket partnership at 156.
The old adage about wickets falling in pairs again proved true when Patel struck a short time later to remove Prasanna Jayawardene for four. Sri Lanka edged ahead with an hour left in the day before Patel grabbed his second, getting Jayawardene for 91.
Once Patel took his third, the introduction of the new ball finished off the hosts' innings when Boult claimed his second scalp with just his second delivery.
