Sri Lanka spinner Maheesh Theekshana took a hat-trick as the home side posted 255-9 off 37 overs, but the tourists could only muster 142 all out off 30.2 overs in response.
It followed New Zealand's comfortable nine-wicket win in Wellington to go 2-0 up in the series, with the third match to be played in Auckland on Saturday.
Sri Lanka's top order has misfired badly in both games.
They slumped to 22-4 at Seddon Park, leaving little chance of reaching their target of 256 in a match reduced to 37 overs each because of early rain.
Kaminu Mendis top-scored with his ODI best of 64 off 66 balls, but fell to a spectacular running catch from Daryl Mitchell from the bowling of Will O'Rourke to seal Sri Lanka's fate.
Janith Liyanage's 22 was the next best score in a Sri Lanka chase marred by two run-outs and a series of risky shots that didn't pay off.
O'Rourke was too quick for the tail, taking 3-31 off 6.2 overs while Jacob Duffy was responsible for some of the early damage, claiming 2-30, including the key scalps of Pathum Nissanka and Kusal Mendis.
Sri Lanka captain Charith Asalanka said their run target should have been achievable.
"I think it was a fair score for batsmen in this kind of small ground, and it's a fair pitch," he said.
"I think again the bad batting in the power play cost us the game."
Earlier, recalled off-spinner Theekshana capitalised on some wayward New Zealand hitting to finish with 4-44 off eight overs.
He removed Mitchell Santer and Nathan Smith with successive deliveries at the end of the 35th over.
The hat-trick was completed -- all from mistimed lofted shots -- when Matt Henry was caught off the first ball of the final over.
It helped to pull back a New Zealand innings which threatened to surpass 300 when opener Rachin Ravindra raced to 79 off 63 balls and Mark Chapman scored 62 off 52.
The pair put on 112 for the second wicket, ending when Chapman holed out to long-off from Theekshana.
Ravindra departed soon afterwards, caught brilliantly at short cover by Asalanka off leg-spinner Wanindu Hasaranga (2-39).
Ravindra, who struck nine fours and a six, believed his balanced batting style was tailored for the 50-over format.
"I do enjoy the ODIs, although you don't see as many games happen anymore, but it's a format I grew up watching, and I think it suits the way I bat," said the 25-year-old, who scored 45 in the first match.
"I think it's a nice, natural tempo being able to go out there and play cricket shots."
