In reply to Australia's imposing total of 559 for nine declared after winning the toss, the Kiwis were dismissed for 624 just before lunch which is their highest ever total against Australia.
At lunch, Australia were yet to score in their second innings, with opener Joe Burns surviving an over from Tim Southee before the break.
Taylor was the last man to fall as he attempted to join captain Brendon McCullum (302 v India) as the only Kiwis to have made 300 in Test cricket.
However, on 290 the right-hander holed out to the substitute fielder Jonathan Wells from the bowling of spinner Nathan Lyon to end a 37-run 10th-wicket stand with Trent Boult (23 not out).
Former skipper Taylor passed several milestones in his innings which was his first century since November last year and ended a form slump that even he admitted was starting to worry him.
He broke 5,000 Test runs and posted the highest ever score by a visiting player in a Test in Australia, as well as becoming the first Kiwi to pass 200 against Australia.
His innings, beating the 287 of England's Tip Foster at the Sydney Cricket Ground in 1903, was the third-highest ever for New Zealand at Test level.
Starc was clearly the best of the Australian bowlers and finished with 4-119.
On the third day, he send down a 160.4 kph thunderbolt that is believed to be the fastest ball ever bowled in Test cricket.

Latest News from Sports News Desk