Roberts, who was awarded player of the match, said it was a huge result for the team.
"It was a massive game for the girls, I'm just so thrilled with the way they fought through the whole game, they're incredible, the girls in front of me," Roberts said.
"It just means so much to every woman in our team, and every single coach. We fought so hard in every single game, we're in a really tough pool, every single team in this pool had exceptional hockey players, and we took every game really hard right till the end."
New Zealand will now avoid having to play in the crossover playoff (for teams ranked second and third in each pool) and get an extended break straight into the quarter-final.
They will face the winner of Germany and South Africa in the last eight next Thursday.
The Black Sticks are currently ranked No 8 in the world. Their best finish at the World Cup was fourth in 1986.