PERTH: Kane Williamson scored a century for the second match in a row as he and Ross Taylor batted through the opening session to drive New Zealand to 249 for two at lunch on the third day of the second test against Australia on Sunday.

The Black Caps still trail Australia's 559-9 declared by 310 runs but 109 runs without the loss of a wicket made it the best session New Zealand have enjoyed so far in the series, which they trail 1-0 after losing by 208 runs in Brisbane.

Ross Taylor, looking more and more comfortable as the day went on, notched up his 25th test half century and reached the break on 82 not out but he was always playing second fiddle to Williamson, who was unbeaten on 120 at lunch.

Resuming on 70 with New Zealand 140 for two, Williamson continued the purple patch of form which has now seen him score four centuries in nine test innings this year.

The 25-year-old showcased his fine technique and assured calmness at the crease as well as his patience when Australia cut off his drives with their field placements.

He brought up his 12th test century when he cracked a 16th four past point before raising his bat, doffing his helmet and hugging Taylor in the now familiarly modest celebration.

There were chances for the Australian bowlers but the uncharacteristically lifeless WACA surface deprived them of a breakthrough.

Immediately after a 15 minute delay when paceman Mitchell Starc decided he wanted to bowl around the wicket but the automatic sightscreen would not move, Williamson, who was on 80, got a thick edge which did not carry to the cordon.

Josh Hazlewood was similarly disappointed when Taylor, on 38, got a big nick on a fine delivery but the ball again hit the deck before it reached captain Steve Smith at first slip.

Taylor made the most of the reprieve and successive fours off Starc a few overs later gave him only his second test half century in nine innings this year.