Daniel Vettori had earlier thrown away his wicket just four runs short of a century to trigger a New Zealand collapse from 254-5 to 295 all out just before lunch at the end of an extended morning session.
Debutant David Warner, however, lasted for just seven balls of the Australian innings before he was despatched for three, while his opening partner Phil Hughes made 10 before he departed to leave the hosts wobbling at 25-2.
Ponting, looking to end a 21-month wait for his 40th test century, showed only flashes of his once brilliant shot-making as he inched his way to 34, while Khawaja headed into the break on 38 and looking in good shape to reach a second test 50.
New Zealand had resumed in the morning on 176-5 with Vettori and Dean Brownlie assiduously extending their sixth-wicket partnership to 158 before the former captain's rush of blood to the head saw him run out.
Vettori, who had taken just four balls of the morning to bring up his 23rd test half century, had smacked a neat four to move onto 96 when he drove a Nathan Lyon delivery to mid-off and set off optimistically for a run.
Michael Hussey gathered the ball and the accuracy of his throw made Vettori's despairing dive academic and sent the 32-year-old trudging back to the pavilion.
Reece Young lasted less than an over before departing for two and Doug Bracewell soon followed for an 18-ball duck with Tim Southee (17) and Chris Martin (one) also failing to keep company with Brownlie, who finished with an impressive 77 not out in just his second test.
Lyon, playing his first match at a ground which traditionally offers little for spinners, took three of the last four wickets to finish with a figures of 4-69.
Australia had two overs to negotiate before lunch and Warner hit a crisp three off Vettori for his first test runs in the first.
Southee, however, brought an early end to his outing with a his first ball, a short delivery that caught the 25-year-old on the gloves and left wicketkeeper Young with an easy catch.
Hughes fell victim to peach of a delivery from Martin and a superb low, diving catch from Martin Guptill at gully but the quality of the delivery will not reduce the pressure on the Australian opener after another failure.
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