New Zealand hit straight back as they exerted pressure on the Samoa line before Kieran Foran finally managed to break through and touch the ball down for the score, while Shaun Johnson slotted over the conversion to fire his side ahead.
The Kiwis thought they had scored just before the break when Manu Vatuvei went over in the corner, but his try was chalked off for an obstruction.
In the second half, Samoa powered ahead when Joseph Leilua made a strong run for the line, and he held off a desperate challenge from Kenny-Dowall to put his side in control of the game, despite Tim Lafai missing his third straight conversion.
New Zealand were becoming desperate as the half wore on, but found their attacking play halted by the resolute defending of the visitors.
The Kiwis upped the ante in the 63rd minute and saw their pressure rewarded as slick play from their backs created space for Jason Nightingale to find space to notch a try, but Johnson failed to level the scores from the ensuing kick.
The home side managed to take the lead with five minutes remaining with another impressive attacking move, as the ball was offloaded four times in quick succession, which allowed Kenny-Dowall to win the game for New Zealand to register their second victory of the competition.