Sri Lankan left-arm spinner Rangana Herath believes the test is still in the balance.
But history would suggest New Zealand is in a dominant position when the game resumes at the University Oval today.
The Black Caps need seven wickets to secure the win after setting the touring side a target of 405.
At stumps on day four, Sri Lanka was 109 for three and needs 296 runs to win.
The partnership between Dinesh Chandimal (31 not out) and captain Angelo Mathews was crucial, Herath said.‘‘If we can [get] kind of a good partnership in the morning session, the game is on,'' he said.
‘‘They are the main experienced batsmen on our side. Chandimal scored some runs in the first innings. I'm sure Angelo will score some runs in this one.‘‘If we can get an 80-100 run partnership, [we will be on] equal terms.''
That said, there have been only four successful fourth-innings chases of 400-plus in history and the touring side lost its last six wickets in the first innings for just 97 runs.
New Zealand began the day on 171 for one with Tom Latham undefeated on 72 and Kane Williamson on 48.
Williamson's dismissal on 71 was mostly down to the prolific right-hander trying to force the pace. The bowler Dushmantha Chameera found the gap between Williamson's bat and pad.
Latham survived a review on 99 and went on to post his third test hundred.
He was joined at the crease by Brendon McCullum when Ross Taylor was bowled looking to attack.
McCullum thumped his first delivery back down the ground for six. It was his 99th in tests and his 100th was not far away.
He walloped Herath over midwicket to draw level with Australian Adam Gilchrist as the leading six-hitter in test history.
He then promptly declared at 267 for three, cutting short the entertainment and setting Sri Lanka a daunting task.
Sri Lanka tried to blunt the New Zealand attack but temptation eventually got the better of opener Dimuth Karunaratne (29).
He forgot the match situation briefly and attempted to loft a short delivery from Tim Southee over gully but got a faint touch.
And shortly before the break, new cap Udara Jayasundera (three) flirted with a short delivery from Neil Wagner and got a tickle down leg. BJ Watling gloved both catches.
Kusal Mendis was dropped on 13 and then again on 25 but was not so lucky third time around.
Four short of his maiden test half-century, Southee found the edge of his bat. Watling dived sharply to his right and intercepted the ball an inch above the grass tops.
It was Watling's ninth catch of the match and equalled the New Zealand record for wicketkeeper dismissals he already shared with McCullum.
The next batsmen in got a few paces out on to the field before the skies unleashed an icy assault just after 5pm. Play did not resume and will start at the earlier time of 10am today.
On Saturday, Sri Lanka's prospects of building a big first-innings score suffered a blow early with the departure of Chandimal before he could add to his overnight score of 83.
Southee, bowling into a blustery northeasterly, got the ball to slant away and take the edge.
He finished with three for 71 and Neil Wagner also grabbed three to help dismiss the touring side for 294.
Mathews' bizarre decision to open the bowling himself along with Suranga Lakmal helped take some bite out of the new ball.
With a test bowling average of around 50 and a strike rate of 105, he was the most unlikely candidate. He was frugal - no problem there - and he actually created a few chances.
But really it felt like an awfully friendly welcome to the crease for Latham and Martin Guptill.
