Mark Craig and Doug Bracewell were both on five not out at tea after Kane Williamson (69), Ross Taylor (35) and Brendon McCullum (0) were all bowled off inside edges playing at deliveries they could have left alone.
Wicketkeeper BJ Watling (11) was dismissed after slashing at a short wide delivery he could also have left.
The hosts had been in control of the match having raced to 141 for two inside the first 40 minutes after lunch, with Williamson and Taylor well set.
Pradeep, however, sparked the collapse when Taylor swayed back to punch a wide off cutter behind point only to get an inside edge onto his leg stump.
McCullum, who scored New Zealand's first test triple century the last time he was at the Basin Reserve, then fell for a two-ball duck when he shaped to cut a delivery from Suranga Lakmal and only succeeded in repeating Taylor's dismissal.
Jimmy Neesham was the only wicket to fall from a good ball when he drove at a Pradeep delivery that moved away off the seam and got an edge to wicketkeeper Prasanna Jayawardene for his third catch.
Watling then slashed at a delivery from Angelo Mathews to be caught by Kumar Sangakkara at first slip for 11, leaving New Zealand 181 for six before Williamson chopped on off Dhammika Prasad one run later.
Pradeep had figures of 3-53 at tea.
New Zealand lost Tom Latham (6) and Hamish Rutherford (37) in the first session, with Rutherford wasting a golden opportunity to build a big score.
Rutherford, who scored 171 on debut against England in early 2013, has not passed 50 since making 62 against West Indies in December 2013 and has accumulated 246 runs in 15 innings at 17.57 since.
(Editing by Peter Rutherford)
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