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The Black Caps were finally dismissed for 412 last night (NZT) after 153 overs of staunch resistance and then had Sri Lanka on the ropes at 43 for three when bad light forced the players from the field seven overs before the scheduled end.
Crucially, Tim Southee (two for 16) and Trent Boult (1 for 16) had knocked off the cream of the Sri Lankan batting order with captain Mahela Jayawardene, the world's No 1-ranked batsman Kumar Sangakkara and opener Tillekaratne Dilshan all out.
A one stage, the home side were reeling at 12-3 and will still be in trouble at 43-3 when play resumes this afternoon (NZT).
The ability of Southee and Boult to find movement through the air and off the pitch troubled Sri Lanka and they will hope there's still a little bit left with the ball 17 overs old. The pitch isn't turning a great deal yet, although spinners Jeetan Patel and Todd Astle could come more into play on the fourth innings.
The last time New Zealand was in such a commanding position was when they beat Zimbabwe by an innings and 301 runs inside three days in January. It's an unfamiliar feeling, especially as they headed into this match hoping to avoid a record-equalling sixth-straight defeat, and a large reason why Williamson said they couldn't afford to get too comfortable.
"[The top three Sri Lankan batsmen] are extremely good quality players and to get them all out before stumps was a fantastic start," he said. "The bowlers have been bowling really well throughout the series and hopefully they can continue that tomorrow.
"I think we are in a good position but, in saying that, it's a very good wicket and you have to bowl this team out twice to get a victory. They have some seriously good cricketers and that's not going to be an easy feat so we are not getting ahead of ourselves. We know we have to turn up and play good sessions each time we go out there."
They have played six mostly good ones so far, including a couple of exceptional ones. Williamson's partnership of 262 was New Zealand's largest in a test in Sri Lanka for any wicket.
The 22-year-old's seven-hour vigil also saw him bring up his third test century in his 18th test and pass 1000 test runs. It was his first ton since his 102 not out against South Africa in Wellington in March and only his second score past 50 in 11 test innings.
For a player considered this country's biggest batting talent since martin Crowe, his lean run had been difficult to take.
"I did a lot of work [between tests] with our batting coach Bob Carter who threw down a lot of balls," Williamson said. "The likes of Brendon McCullum also helped me to get my head around a few things.
"I haven't scored for a few tests so they all helped out and have been really good and supportive. They helped with preparation so it was nice to get the word from them about how things play out and then take it into this match.
"[The record partnership with Taylor] was satisfying, but more the fact it allowed us to get over 400 runs because it puts us in a good position in the match."
For a team who might have hoped rain would save them on a few occasions, they will hope it stays away. Showers are forecast in Colombo for each of last three days.