Starc's top speed, and he did work up real pace in that spell, also included balls which broke McCullum's bat and which had McCullum dropped at slip by Nathan Lyon.
By tea, New Zealand were 406 for three, with Taylor, marching towards what would be his second test double century, on 165, and captain Brendon McCullum, after a sketchy start, on 21.
New Zealand trailed Australia by 153 runs.
Taylor, who had given just one chance, did have the occasional worrying moment, but as his century approached and for a time after that, he was in complete command. Boundaries flowed as Australia's bowlers ran out of ideas. By tea he had hit 26 of them in his 213-ball hand.
The only wicket of the day had been Kane Williamson, out to a tired pull shot at a ball from seamer Josh Hazlewood to be caught at mid on for 166.
It was a fine performance by Williamson, his 12th test ton, and 22 runs short of equalling Martin Crowe's New Zealand record against Australia.
Taylor and Williamson put on 265 for the third wicket, a New Zealand record for any wicket against Australia, eclipsing the 253 of Nathan Astle and Adam Parore on the same ground for the eighth wicket 14 years ago.
Most importantly, from New Zealand's perspective they had put their side in a solid position to at least save the test, which would give them a chance of squaring the series in the final test at Adelaide.
Although the pitch is flat and desperately hard work for the bowlers, there could still be some fun left in the next two days. Declarations might become important.