Martyn scored 106 not out and shared an unbroken 90-run partnership with Adam Gilchrist to guide Australia to 337 for five in their first innings when play ended.
Gilchrist finished the day on 45 from just 47 balls and eyeing another big score after his blazing first Test century.
With the first day washed out because of heavy rain, the Australians seemed intent on making up for lost time after being sent in to bat by Stephen Fleming.
New Zealand briefly pegged Australia back with three quick wickets after lunch but Martyn put the visitors back in control with his hundred.
Martyn, who scored six Test centuries last year, was on 24 at tea before he accelerated his scoring in the final session, bringing up his century off 173 balls with 16 boundaries.
Martyn shared an 84-run stand with Simon Katich who made 35 then 90 with Gilchrist who helped himself to seven fours and a six as the Australians piled on 163 runs in the last session.
The New Zealand bowlers failed to make the most of the conditions after getting first chance to bowl on a wicket that had been covered for two days.
Left-arm seamer James Franklin captured two wickets but the pick of the bunch was left-arm spinner Daniel Vettori, who took 2-74 from 29 overs.
Vettori made the breakthrough before lunch when he had Langer caught behind with the total on 82 then claimed Australian skipper Ricky Ponting for nine after the re-start, trapping him leg before wicket with a ball that straightened.
Hayden, who was unusually cautious, passed his 50 after lunch but fell with the total on 146 when he hit an easy catch to Lou Vincent at cover, giving Franklin his first success.
Michael Clarke was also subdued, making eight off 32 balls, when he was caught in the slips off Nathan Astle before tea. Franklin dismissed Katich after tea but that was New Zealand's last positive note of the day.
Australia first innings
J.Langer c McCullum b Vettori 46
M.Hayden c Vincent b Franklin 61
R.Ponting lbw b Vettori 9
D.Martyn not out 106
M.Clarke c Fleming b Astle 8
S.Katich c McCullum b Franklin 35
A.Gilchrist not out 45
Extras (b-4 lb-8 w-2 nb-13) 27
Total (for five wickets, 98 overs) 337
To bat: S.Warne, J.Gillespie, M.Kasprowicz, G.McGrath Fall of wickets: 1-82 2-100 3-146 4-163 5-247 Bowling: Martin 21-5-79-0 (nb-5), Franklin 23-4-94-2 (nb-8 w-2), O'Brien 17-4-64-0, Vettori 29-5-74-2, Astle 8-2-14-1