While India eventually prevailed, Southee set about repeating that effort in a devastating first spell with the ball at the Galle International Stadium.
The 23-year-old struck just before stumps yesterday to remove Dimuth Karunaratne and give New Zealand hope after a disappointing day with the bat, and he turned that hope into real promise in his first six overs on day two.
Southee 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 Brendon McCullum at third slip and, after he dropped a simple catch, Martin 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, Jayawardene and Mathews came together.
Jayawardene had to survive a couple of strong LBW shouts, one from Boult and the other from Southee, before knuckling down to blunt the Black Caps bowlers. Both he and Mathews brought up their half-centuries, flourishing against the ineffective Doug Bracewell, James Franklin and Jeetan Patel.
By the time tea was called the pair had put on 140 for the sixth wicket, providing their side with the big partnership New Zealand's innings was lacking.