New Zealand will take a 127-run lead into the final day of the first Test after bowling Sri Lanka out for 498 and reaching 64-2 in their second innings.
Sri Lanka made their highest total in a Test against New Zealand despite losing their last four wickets for 10 runs.
But with only three sessions left, the match looks to be heading for a draw.
Mahela Jayawardene's dismissal for 141 triggered Sri Lanka's collapse as Chris Martin and James Franklin finished with four wickets each.
New Zealand had 30 overs to face before the close and lost Craig Cumming for 16 and first innings centurion Hamish Marshall for six.
Both fell lbw to Lasith Malinga, whose unorthodox slinging action again caused problems for the Kiwi batsmen.
Marshall's brother James survived to reach 33 not out and he managed to keep night-watchman Paul Wiseman away from the strike in the final two overs before the fading light forced a halt.
Sri Lanka had started the day 210 runs behind but Jayawardene and Thilan Samaraweera were well set on 118 not out and 34 respectively.
They extended their fourth wicket partnership to 122 before Jayawardene got a thick edge to a swinging delivery from left-armer Franklin with the total on 407 and was caught behind.
He faced 243 balls during his innings, his second Test century against New Zealand and 13th in all, and hit one six and 19 fours.
Tillakaratne Dilshan also departed before lunch, caught in the covers by Lou Vincent off Martin for 28, and the fast bowler (4-132) was celebrating again soon after the re-start when he added the wicket of Samaraweera.
He was caught by Stephen Fleming for 88 with the total on 463 and the tail followed in quick succession.
Chaminda Vaas fell to off-spinner Wiseman for 17 but the three remaining wickets were all taken by Franklin, who reaped the benefits of bowling to a full length to finish with figures of 4-126.
New Zealand: Stephen Fleming (Capt), Craig Cumming, James Marshall, Hamish Marshall, Lou Vincent, Nathan Astle, Brendon McCullum, James Franklin, Kyle Mills, Paul Wiseman, Chris Martin.
Sri Lanka: Marvan Atapattu (captain), Sanath Jayasuriya, Kumar Sangakkara, Mahela Jayawardene, Thilan Samaraweera, Tillakaratne Dilshan, Upul Chandana, Chaminda Vaas, Nuwan Kulasekara, Lasith Malinga, Rangana Herath.
Umpires: Darrell Hair (Australia), Steve Bucknor (West Indies).