New Zealand were under pressure at 14-2 before skipper Taylor and Kane Williamson (95 not out) led the recovery with an unfinished 199-run stand for the third wicket at the P. Sara Oval in Colombo.
Taylor and Williamson denied Sri Lanka success in the afternoon session with their responsible batting against both pace and spin on a good pitch as the tourists added 79 to their lunch total of 96-2.
Sri Lankan left-arm spinner Rangana Herath, who took 11 wickets in his team's 10-wicket win in the first Test in Galle, was pressed into the attack after 14 overs but failed to keep pressure on Taylor and Williamson.
Herath has so far conceded 44 runs in his 21 wicketless overs as the New Zealand pair took no risks during their big stand, patiently waiting for loose deliveries to punish.
Williamson cut and then drove Herath through the covers for two fours in an over before completing his sixth Test half-century.
The New Zealand captain played some aggressive shots, including two fours in an over from paceman Shaminda Eranga, and reached his 17th Test half-century with a boundary off the same bowler immediately after the lunch-break.
New Zealand made a poor start as they lost openers Martin Guptill and Brendon McCullum in the first four overs.
Guptill was caught by Angelo Mathews at first slip in Nuwan Kulasekara's opening over, while McCullum was unlucky to given out leg-before off Eranga as TV replays suggested he had inside-edged the delivery on to his pad.
Guptill and McCullum each scored four.
Sri Lanka made one change from the side that played the last Test, replacing Dimuth Karunaratne with fit-again opener Tillakaratne Dilshan.
The tourists brought in debutant leg-spinner Todd Astle in place of all-rounder James Franklin.
Ross Taylor, Kane Williamson boost New Zealand against Sri Lanka
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