Katich was unbeaten on 67 as the home side ended play on 131-6 in their second innings, a lead of 189.
A total of 16 wickets fell in the day with New Zealand earlier bowled out in 50 overs for just 156.
Ross Taylor's 40 was the top score as left-arm paceman Mitchell Johnson returned figures of 4-30.
The tourists had the better of the opening day as they bowled Australia out for 214 but their batting line-up was also found wanting on a seamer-friendly surface.
Stuart Clark made an immediate breakthrough when his first delivery of the day bounced awkwardly and accounted for Aaron Redmond, who was caught by Ricky Ponting at second slip for three.
Redmond's opening partner Jamie How was bowled by Brett Lee for 14 and all-rounder Shane Watson then had Jesse Ryder caught behind for 30 as he tried to square cut.
Johnson picked up his first wicket in the following over when Brendon McCullum was taken by Ponting for eight froma ball angled across him towards the slips and only Taylor demonstrated any kind of fluency for the Kiwis as he collected seven boundaries.
But his 51-ball cameo came to an end when he was adjudged lbw to Lee and after Watson bowled Grant Elliott for nine, the last four wickets fell for 13 runs in the space of four overs.
Daniel Vettori, Tim Southee and Iain O'Brien all fell to Johnson before Clark bowled last man Chris Martin with a yorker, leaving Daniel Flynn high and dry on 39 not out.
Australia's delight at earning a 58-run advantage quickly turned to concern at the start of their second innings as Martin found the edge of Matthew Hayden's bat and the big opener departed for a first-ball duck.
Worse followed when O'Brien dismissed Ponting and Mike Hussey in the same over, Ponting caught by Redmond for 17 after mis-timing a pull shot and Hussey given out caught behind to register only the second nought of his Test career, although TV replays suggested he was unlucky with the decision.
The home side could not afford the needless run out of Michael Clarke, who was beaten by Redmond's direct hit from square leg after making only nine, but Katich and Symonds managed to steady the ship by adding 56 for the fifth wicket.
katich finally brings decent score to the australia.
Katich reached his half century off 86 balls but the partnership came to an end when Symonds, on 20, tried to hook a short ball from Martin and edged to McCullum.
There was more good news for New Zealand shortly before the close as Martin (3-52) had Watson lbw for five, leaving the match intriguingly poised
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