Ramnaresh Sarwan, on 13, was caught behind down the leg-side off seamer Chris Woakes, who struck again when acting captain Denesh Ramdin could only fend a rising delivery to Ian Bell in the slips.
But while the left-armer took the bulk of the wickets for his side his fellow seamer Ishant Sharma (one for 47 off 14 overs) always made life difficult for the hosts and was eventually rewarded with the scalp of Black Caps skipper Daniel Vettori for a 13-ball 11.
Australia had made 505-8 declared in their first innings before dismissing the home side for 177, largely thanks to seamer Ben Hilfenhaus, who took 5-47.