Matt Henry and Ajaz Patel added 104 runs for the last wicket after a century by opener Devon Conway set up the innings on the first day.
Earlier, Naseem took the day’s first wicket when he bowled Ish Sodhi for 11 — a ball that cut through sharply and beat the batter completely.
Blundell, who was 30 overnight, reached his fifty with a boundary and a single off Abrar Ahmed. He hit six boundaries in his 51 before he was bowled by Ahmed.
The spinner then had Tim Southee stumped for ten, before Henry and Patel prolonged the innings, helping New Zealand cross the 400-mark.
Henry has so far smashed six boundaries and two sixes in his 59-ball knock. Agha Salman (3-66), Naseem (3-71) and Ahmed (3-142) were the main wicket-takers.
Agha Salman (3-66), Naseem (3-71) and Ahmed (4-149) were the main wicket-takers.