Lahiru Thirimanne drove early to spoon a catch to mid off while captain Angelo Mathews had a rare failure, being caught behind off Tim Southee for 15.
Wicketkeeper Prasanna Jayawardene was out in the final over, edging Bracewell to third slip.
Key batsman Kumar Sangakkara had battled through to stumps, having passed 12,000 test runs when he reached five, and was on 33 at the end of the day.
Only India's Sachin Tendulkar (15,921 runs), Australian Ricky Ponting (13,378), South African Jacques Kallis (13,289) and India's Rahul Dravid (13,288) have scored more than the classy lefthander. However Sangakkara was fastest of the quintet to 12,000 by at least 23 innings.
He had a life on 20 when he slipped setting off for a run and would have been run out at the bowlers' end had the throw been accurate or a fielder been up at the stumps. Twice he got inside edges to Bracewell deliveries which flew past his leg stump.
Earlier Sri Lanka's bowlers were guilty of wasting the new ball in the first session, but made up for it in the middle period as three New Zealand batmen conspired to play balls onto their stumps and Nuwan Pradeep and Suranga Lakmal led a much improved seam bowling performance.
Kane Williamson was the pick of the New Zealand batsmen, continuing his fine form to reach 69.
Pradeep, who missed selection for the first test, which New Zealand won by eight wickets, finished with his best test figures, four for 63 while Lakmal took three for 71.
