They were bothered by the seam and bounce on offer at Seddon Park.
Meanwhile, Shubman Gill, who is also vying for a berth, managed a duck.
However, on Day 2, Agarwal (35*) and Shaw (23*) showed a better approach and played positively.
Both had strike-rates of over 100.
India bowlers do not allow NZ XI to get away
For New Zealand XI, nobody went on to get past the 50-run mark. Several batsmen threatened after getting positive starts, however, Indian bowlers managed to hit back at crucial junctures and claim wickets. This derailed the NZ XI side. Henry Cooper (40) led the show.