New Zealand have made an unbeaten start to their second innings as the second session of a controversial day two ended in their third Test against Australia in Adelaide.

The Baggy Greens began the day at 54-2 with Steve Smith and Adam Voges unbeaten at the crease, but Voges was to fall for 13 to the bowling of Tim Southee.

Shaun Marsh and Mitchell Marsh departed quickly, adding just six runs between them, leaving the Aussies at 80-5.

Smith held his composure at the crease to notch his half-century, guiding his team past the 100-run mark in the process. However, he was then caught behind for 53 off the bowling of Mark Craig.

The skipper's dismissal sparked a collapse as Peter Siddle and Josh Hazlewood followed him back to the pavilion.

Controversy then reigned at the Adelaide Oval when Nathan Lyon appeared to edge the ball behind to slip off the bowling of Mitchell Santner, although the decision was given not out on the field.

New Zealand reviewed the call and hot-spot appeared to show a mark where the ball struck the edge of the bat, leaving Lyon to make his way off the field.

However, third umpire Nigel Llong opted to give the decision not out to the bemusement of Brendon McCullum and his team as Lyon returned to the crease.

Peter Nevill and Lyon then added insult to injury by taking the attack to the Kiwis, powering their way over the 150-run mark, putting together a ninth-wicket partnership of 74 before Lyon was out for 34.

Nevill reached his half-century as Australia edged past the Kiwis' first-innings total before the injured Mitchell Starc crashed 20 off one over to take his side into the lead.

The Baggy Greens' innings ended on 224 when Nevill was out for 66 to Doug Bracewell, giving the hosts a lead of 22 runs.

New Zealand openers Martin Guptill and Tom Latham guided their side to 22-0 before the break, erasing Australia's lead ahead of the final session of the day.