The classy lefthander tried to hook a short ball but sent it straight to Boult just inside the fine leg boundary.
Boult put Jayawardene through hoops before having him caught by Kane Williamson at gully to have the hosts reeling at 12 for three.
Opener Tharanga Paranavitana was on nine from 39 balls while Angelo Matthews, helped by three fours in one Southee over, had reached 20. Bad light cut the day short by seven overs.
That New Zealand reached 412 was down to the 262-run third-wicket stand between captain Ross Taylor and Kane Willliamson, New Zealand's largest in a test in Sri Lanka for any wicket, plus a couple of useful late-innings stands.
Taylor made 142 off 306 balls, Williamson completed his third test century after a shaky start last night, finishing with 135, having batted seven hours and faced 305 balls.
Both went LBW trying to sweep left arm spinner Rangana Herath and the veteran, enjoying a fine run of success, went on to finish with six for 103. All six were either bowled or lbw.
Todd Astle's first test innings lasted 36 balls, for three, and wicketkeeper Kruger van Wyk was out for a duck.
However Daniel Flynn batted grittily to complete his sixth test half century, making 53 before going LBW to Herath.
He shared a 46-run stand with Doug Bracewell, put on a further 28 with Southee and finally 36 with Jeetan Patel.
Herath, who took 11 wickets in Sri Lanka's 10-wicket win at Galle, completed his 13th bag of five or more wickets in his 42nd test.
But New Zealand have the whip hand, courtesy of Southee and Boult.