At tea on the third day New Zealand had lost both openers and faced an uphill battle, requiring a further 291against an Australian attack brimming with confidence.
The fourth innings began perfectly for Australia when Lee struck in the first over to become the fourth Australian to reach 300 Test wickets. Lee drew Jamie How into a drive and the ball flew off the edge to second slip, where Ricky Ponting completed the task.
New Zealand"s chase took another blow when Aaron Redmond fell to a sharp return catch from Clark, who juggled the take on the second grab to leave the visitors at 2 for 30 and relying on Jesse Ryder and Ross Taylor.
New Zealand were frustrated not to be chasing a target closer to 250 after they allowed Australia last two pairs to add 82. Katich combined with Mitchell Johnson for an invaluable 53-run stand that featured some clean striking from Johnson, who struck three fours and a powerful six over the head of the bowler Daniel Vettori
When Johnson miscued an attempted pull off Grant Elliott and slapped the ball to mid-off for 31 the problems did not end for New Zealand. Clark kept the boundaries coming - he hit four in his 12-ball 18 - in a 29-run partnership that ended when he drove to mid-off to give Tim Southee his only wicket of the innings.
It left Katich on 131 and he became the first Australian to remain unbeaten through a completed Test innings since Mark Taylor in Adelaide in 1997-98. Katich"s outstanding innings was just what Australia required, especially when the top order had stumbled to 6 for 115.
It was his fourth Test century since his recall earlier this year and he finished with a remarkable 48.8% of Australia"s total of 268. He was bogged down early in the morning but grew in confidence and raced through the 90s within seven balls.
Southee was driven for a four that went so straight that the umpire Billy Doctrove had to hurdle it and the next ball Katich rolled the wrists perfectly in his textbook hook that smashed into the turf and flew away for four more.
The century came up with another boundary from his 179th delivery when he guided another hook very fine off Iain O"Brien and Katich"s joy was understandable.
It had been at the same venue in 2005 that he failed against West Indies in what was his last Test for nearly three years - and could have easily been his final of all time - but since his return in May he has tripled his career tally of Test hundreds. He punched through gaps with confidence and struck 16 fours, making it hard to understand how none of his top-order friends could pass 20.
Katich did survive a couple of lucky moments but they came when he was already well set. O"Brien put down a hard but catchable return chance when the batsman had 70 and Ryder at short leg also missed a sharp but gettable opportunity off Vettori when Katich was on 86.
On a surface that was not as bad as the scorecard indicated the mistakes were not fatal for New Zealand, but they were costly.
Australia added 89 in the first session for the loss of two wickets and the support he received from Johnson in the lead-up to lunch to was critical.
Johnson flicked Vettori for consecutive boundaries through and over the leg-side field and helped ease the threat from Vettori, who had made both the breakthroughs in the opening session.
Lee found a novel way to get out when his inside edge squeezed between his legs and onto the stumps - had he been wearing inner-thigh pads the ball might not have got through. Vettori had already disturbed the stumps of Brad Haddin, who played the wrong line to an arm ball and was out for 19.
The lack of potency from New Zealand"s seamers on the third day helped Australia"s batsmen but could have been a concern for their four-man pace attack.
However, the strong start from Lee and Clark made the challenge all the tougher for New Zealand, who need to more than double their first-innings 156 to pull off their first win in Australia since 1985.