They didn't. The Maori agricultural complex is largely confined to the north island, where sweet potatoes could successfully be grown. On the south island they adopted a hunter gatherer subsistence strategy (this is a major simplification of course--parts of the south island were suitable for cultivation and forms of horticulture were practiced throughout, and of course in the north island hunting and fishing still formed significant portions of the diet). This is why the distribution of pa and other large earthworks is so heavily skewed towards the north island.

An interesting note is that agriculture was not immediately adopted as the main subsistence strategy even in the north. The first "phase" of Maori habitation was actually dominated by moa hunting, as the birds and their eggs formed a ready source of food. Heavy agricultural exploitation waited until after that food source was exhausted. This is actually a patterns seen in many areas of the Pacific, with an early phase characterized by a heavier reliance on hunting and gathering followed by a intensification of agricultural practice with the "filling" of the islands.

Sources for this is Peter Bellwood's First Farmers and Patrick Kirch's Road of the Winds.

The key difference between agriculture in NZ and the rest of Polynesian was the absence of both coconuts and taro, staple crops in Polynesia, which do not grow in the colder NZ climate.

Instead, Maori cultivated kumera (sweet potato) and yams, both of which they bought to NZ with them, in much larger quantities than they were grown in the rest of the Pacific. Kumera and yams can both survive and grow well in the NZs climate. They also cultivated the (native) cabbage tree, which is good source of both sugar and carbohydrates.

Along with these crops, Maori ate fish and birds, and the roots of (native) fern trees.