New Zealand took immediate advantage of Samoa being down to six men by finding the extra player out wide as Caleb Tangitau ran in for the opening try. Regan Ware added a second a few minutes later to give New Zealand a 10-0 lead, as it looked they would run away with the contest.
But Samoa showed great fight with Steve Rimoni scoring an impressive individual try from long distance to reduce the lead to 10-7 before Akuila Rokolisoa scored in injury time to give New Zealand a 10-point lead at the break.
Samoa managed to outscore New Zealand in the second half with a Vaa Apelu Maliko double and another try to Owen Fetu.
Samoa will play group D winners Argentina in the quarter-finals while the other group matches are yet to be completed.
In the early games, New Zealand shared the tries around with six different scorers in both wins against Japan and Wales.