Australia 454 and 0 for 40 (Warner 23*, Burns 16*) lead New Zealand 251 (Phillips 52, Latham 49, Lyon 5-68, Cummins 3-44) by 243 runs

Nathan Lyon demonstrated why he had been so dismissive of the notion that he might be rested for the New Year's Test by scything through New Zealand with his maiden five-wicket haul at the SCG. There were times on Jane McGrath Day, though, when the added assistance of Mitchell Swepson as a wrist-spinning offsider would not have gone astray.

Australia claimed a first-innings advantage of 243 by the end of a day of considerable smoke haze in Sydney, though not enough to force a suspension in play. The Australian Prime Minister, Scott Morrison, had been originally scheduled to watch day three's play, but was otherwise occupied in his rapidly escalating response to the bushfire crisis sweeping the rest of the country.

Pat Cummins started 2020 as he had ended 2019 with another incisive display, but it was Lyon who played the central role in cutting through the visitors' top and tail on a pitch taking increasing amounts of spin. Mitchell Starc delivered a couple of threatening spells, but the third seamer, James Pattinson, found little to enjoy in the pitch and might easily have had his 16 overs for 58 runs, including nine boundaries, subbed out for Swepson's legbreaks and googlies.

Lyon defeated Tom Blundell and Jeet Raval before Cummins coaxed Tom Latham into a chip straight into the hands of mid-on, undoing some of the good work of the touring side's openers who had reached 68 without loss. Cummins pinned Ross Taylor lbw shortly after lunch, before BJ Watling dragged Mitchell Starc onto the stumps and Colin de Grandhomme ran himself out.

Things may have been worse for New Zealand, however, as Lyon dropped two straightforward return catches offered by the debutant Glenn Phillips and needed treatment for a cut to his right thumb after the first of them. Phillips survived no fewer than three chances on his way through to tea, the last of which a dismissal, caught in the deep off James Pattinson, that was ruled out by the subsequent ruling of a no-ball from the paceman.

A fifty on Test debut with still a meritorious effort from Phillips before his dismissal, bowled through the gate by Cummins, ushered a rapid end to the innings.

Resuming at 0 for 63, the visitors made slow progress through the first half an hour, before Blundell misjudged a cross-seam delivery from Lyon and was bowled between his legs as he tried a shovel-pull shot to the leg side. Raval, who had been waylaid earlier in the Test with flu-like symptoms, walked out to play with far greater fluency than he had offered in the Perth Test, and for a time the scoreboard moved quickly.

Lyon, though, was able to skid a stumps-seeking delivery into Raval's front pad, winning an lbw verdict from Aleem Dar. Raval took a long time to review, appearing to use up more than his allotted 15 seconds, but Aleem allowed a decision referral that showed the ball striking legstump.

Latham's occupation ended the very next over when he miscued a Cummins delivery that held in the pitch and resulted in a simple catch for Mitchell Starc, and Phillips may well have followed had Lyon been able to hold onto a caught-and-bowled. Taylor hammered Travis Head's offbreaks for a pair of boundaries in the final over of the session, but he was unable to last long after the interval as Cummins extracted enough reverse swing to bend the ball around his bat and strike him just in line with the off stump.

Watling was becalmed before Starc managed to coax him into an expansive drive that only saw the ball edged back onto the stumps, and de Grandhomme dawdled too much over a second run to be dismissed through Matthew Wade's throw and Tim Paine's clean handling behind the stumps.

Phillips enjoyed plenty of good fortune in getting through to tea, but it was little less than he deserved having been flown in for his Test debut the day before the match due to the spate of injury and illness affecting the New Zealand squad. The second new ball was now available to the Australians, and eventually Cummins found the ideal line and length to burst through Phillips, knocking back the offstump.

Lyon defeated Will Somerville and Neil Wagner in the space of three balls, the former beaten twice before he was bowled, and then Matt Henry was alertly stumped by Paine when his defensive shot dribbled behind the stumps.

David Warner and Joe Burns had very little trouble gliding to the close and adding another 40 to Australia's advantage, but rain forecast for day four may complicate Paine's declaration plans.