Sri Lanka were closing in on wiping out their 303-run first innings deficit with seven wickets in hand when Boult brought their cautious progress at Christchurch's Hagley Oval to a halt.
He removed the defiant Karunaratne for 152 and Niroshan Dickwella for four as Sri Lanka were reduced to 293-5 at stumps, still 10 runs from making New Zealand bat again.
Angelo Mathews is not out 53 with Tharindu Kaushal on five while Boult, New Zealand's chief wicket-taker, has three for 62.
Karunaratne was annoyed with his dismissal which came as he was about to appeal against the fading light.
"The light was a bit low. Boult was bowling beautifully at that time. I wanted to tell the umpires it was difficult to bat and just get to the dressing room," he said.
Karunaratne believed a lead of 150 was possible for Sri Lanka and would be competitive on a turning wicket.
But New Zealand wicketkeeper BJ Watling said Boult's late double strike kept the initiative with the Black Caps.
"To make the bang-bang tonight put us back in the position where we look comfortable," said Watling .
"They obviously fought hard and played some good cricket but, all-in-all, 200 runs and five wickets in a day and they're still behind us that's a good day for us."
Karunaratne's wicket was vital for New Zealand after the 26-year-old had stood in 87-run partnership with Lahiru Thirimanne (25) for the third wicket and then a 97-run stand with Angelo Mathews.
The left-hander had been under enormous pressure after making a four-ball duck in Sri Lanka's first innings paltry 138 in reply to New Zealand's 441 and were forced to follow on. But he easily surpassed his previous Test best of 85.
Sri Lanka were in trouble when they lost two quick wickets at the start of the third day, including another failure by the world's top-ranked batsman Kumar Sangakkara, who fell for one.
But if New Zealand's hopes were up with Sri Lanka at 94-2 and trailing by 209, Karunaratne had other ideas.
With survival foremost in his mind he batted for a shade over eight hours and faced 363 deliveries in his marathon knock which included 17 fours.
Karunaratne started the day on 49 with Sri Lanka 84-0 and reached his fifth half century with a single off the second ball.
Kaushal Silva was caught behind four balls later without adding to his overnight 33 and Sangakkara followed soon after.
It was a disappointing outcome for Sangakkara, the most prolific batsman in the world this year with 1,493 runs from 22 innings, including a fifty in each of his past nine Tests.
He could only manage seven from his two innings and remains six runs short of becoming the fifth member of the exclusive group of Test cricketers to score more than 12,000 runs.
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ