New Zealand took full command on day two when they bowled Sri Lanka out for just 138 in reply to the hosts' first innings total of 441 in Christchurch.
Sri Lanka fought back to within 10 runs on day three as Dimuth Karunaratne's maiden Test century helped the tourists to 293-5 at stumps.
It remains a tall order for Sri Lanka to rescue the match, though, and seamer Trent Boult (3-62) claimed the wickets of Karunaratne (152) and Niroshan Dickweller (4) in his final session to leave New Zealand well poised.
And wicketkeeper Watling praised the hard work of New Zealand's attack.
"That final spell was a great example of how much the bowlers have improved," he said. "Tim [Southee] did not get the rewards and Trent did.
"To come that hard after 30-odd overs, and get enough nip, swing and ask a lot of questions was great. He did that to the new guys coming in as well, and put them under pressure.
"They definitely batted a lot better. Karunaratne played extremely well to deny us his wicket for the majority of the day, and it took a great delivery from Trent to finish him off.
"It was frustrating not to get him. He played an exceptional innings in the circumstances."
While the odds are stacked against Sri Lanka, Karunaratne believes that with skipper Angelo Mathews (53 not out) at the crease, and Prasanna Jayawardene still to come, the match can still be saved.
"We saw, in the latter part, some turn in the wicket," he said.
"Angie [Mathews] is there and Prasanna also is there. If we can score another 150 to 175, it would be a good score with this wicket.
"If the fast bowlers can get a few wickets with the new ball then we will be in a good position."