Fulton, in only his second outing in New Zealand colors, was not out 70 at the end while How on debut made 58 as the home side easily chased down their target of 164 runs in just 37.2 overs.
It was not a difficult target on a pitch which held no dangers, but the way Fulton and How put on 95 for the third wicket showed an authority which not even the experience of Chaminda Vaas and Muttiah Muralitharan could ruffle.
Opener How saw his first two partners - senior batsmen Lou Vincent and Nathan Astle - back in the pavilion by the 11th over and at two for 41, Sri Lanka could smell an outside chance of success.
But Fulton had other ideas. After taking time to read the rhythm of Muralitharan, he opened up with a majestic array of shots around the ground, scoring 70 off 79 balls including seven fours and a towering six.
As his confidence grew, so did the 24-year-old How's, and they put New Zealand in an unbeatable position before How paid the price for a loose shot to Sanath Jayasuriya and was clean bowled, leaving Hamish Marshall to partner Fulton through the final 30 runs.
New Zealand captain Daniel Vettori said his bowlers did well to contain Sri Lanka but there was no doubt who won the game.
"When two new guys come into the team you want them to succeed, but when the two new guys go and win the game for you that's extremely pleasing and that's what they did," he said.
Earlier, the New Zealand pace attack had throttled the Sri Lankan batsmen, leaving the tourists all out for 164 in the 48th over. Captain Marvan Atapattu said there were no excuses for the disappointing effort.
"Once you got in it was a beautiful wicket to bat on," he said, pointing the finger directly at his under-performing batsmen.
"The ones who are getting runs are not getting enough and those who aren't getting runs are not getting anything at all."
South Africa to get aggressive
Paceman Andre Nel says South Africa may copy Australia's aggressive appealing to match umpires in Monday's final cricket Test at the Sydney Cricket Ground.
Nel, the firebrand bowler of the Proteas team, said that if Australian bowlers like leg-spinner Shane Warne can get away with it, then maybe South Africa should follow suit.
"I think they are very, very clever about the way they do things with umpires," Nel told reporters at Sydney Airport yesterday.
"They put a lot of pressure on the umpires and sometimes it counts in their favor. Maybe we can learn something from them in a certain way by doing this.
"But sometimes they go a bit overboard and it gets a bit annoying, but that's the way they do it and it's working for them," he said.
Nel, who is set to share the new ball with Shaun Pollock in the injury absence of Makhaya Ntini, said South Africa could learn from the much debated appealing style of the Australians.
Warne pushed the line with his aggressive appealing in this week's second Test victory over South Africa in Melbourne but he had not been reported by the umpires, match referee Chris Broad said after the Test.
South African coach Mickey Arthur said Warne was a master at pressuring the umpires but Broad rejected suggestions that he should face disciplinary action for his robust appealing, particularly to rookie Test umpire Asad Rauf of Pakistan.
"If they can get away with it, why can't we try and get away with it too," Nel said. "Maybe we can try and put pressure on umpires, inexperienced umpires, which they do very, very well. Maybe we can learn from them to do that better."
Meanwhile newly-arrived Johan Botha was shielded from the media at the airport.
Off-spinner Botha, 23, who has yet to play a Test, joined the team last Thursday and could partner established spinner Nicky Boje in the third Test on the likely spin-friendly Sydney pitch.
South African officials said they didn't want to subject Botha to undue media pressure.
"He's a surprise package, you've just got to wait and see," Nel said.
Nel also said he was looking forward to opening the fast bowling attack alongside Pollock.
"It's always nice to get the chance with the new ball and to bowl with Polly," Nel said.
Renowned for his manic facial expressions in the field, Nel said he was enjoying his interaction with Australian crowds, who were jeering him, but also seeking his autograph.
"I enjoy having a bit of fun with them," Nel said. "You've got to relate to the crowd."