The New Zealand openers, Bryan Young and Blair Pocock, survived a nervous three overs against the new ball to guide the tourists to 4 for 0 at the close, but still needed another 315 to pull off what would be a memorable victory.
Accurate bowling by New Zealand's inexperienced but disciplined attack delayed Taylor's declaration - at 294 for 6 - until 20 minutes before close of play at The Gabba.
The tourists restricted the scoring rate to little more than two runs an over before tea as Australia's No 3, Greg Blewett, amassed a patient 91 to anchor the innings.
Only late on - when Ricky Ponting and Paul Reiffel launched an assault - did the batsmen gain the upper hand on a placid wicket. Ponting remained unbeaten on 73 off 84 balls after smashing two sixes and seven fours against a tiring attack. The Tasmanian was visibly frustrated at being denied the opportunity to record only his second Test century because of the timing of Taylor's declaration.
With the pitch slowly deteriorating and offering more encouragement for the bowlers, Australia's leg-spinner Shane Warne could emerge as the key figure today.
"I give us more than a reasonable chance," New Zealand's coach, Steve Rixon, said. "It will all get down to a solid base. We can't be three for diddly at the start.
"It's amazing how quick runs come in the last session if you have got wickets in hand. I apologise to all those people who booked golf tomorrow."
Fourth day; New Zealand won toss
AUSTRALIA - First Innings 373 (M A Taylor 112, P R Reiffel 77).
NEW ZEALAND - First Innings 349 (S P Fleming 91, C L Cairns 64, C D McMillan 54).
AUSTRALIA - Second Innings
(Overnight: 25 for 1)
M T Elliott c Fleming b Vettori 11
I A Healy c Fleming b Allott 25
G S Blewett c Fleming b Cairns 91
M E Waugh c Fleming b Vettori 17
S R Waugh c Parore b Cairns 23
R T Ponting not out 73
P R Reiffel not out 28
Extras (b1, 4lb4, w5) 10
Total (110.5 overs, for 6 dec) 294
Fall (cont): 2-6, 3-72, 4-104, 5-163, 6-217.
Bowling: Doull 19-5-44-0; Allott 19.5-4-60-1 (nb2); Cairns 16-4-54-3 (nb3); Vettori 36-13-87-2; Harris 9-0-30-0; Astle 1-0-14-0.
NEW ZEALAND - Second Innings
B A Pocock not out 3
B A Young not out 0
Extras (nb1) 1
Total (for 0) 4
Bowling: McGrath 2-0-3-0 (nb1); Kasprowicz 1-0-1-0.
Umpires: S Randell (Aus) and V Ramaswamy (Ind).Reuse content