Khawaja was unbeaten on 68 and debutant Finch was unbeaten on 59 at the break, both having survived some anxious moments against a threatening Yasir Shah on a Dubai stadium pitch which has started to take spin.
Australia trail Pakistan's first innings total of 482 by 345 runs with all their wickets intact.
Finch looked confident as he punched two boundaries and a six off Yasir before sweeping off-spinner Bilal Asif for a boundary to reach his half-century.
He has so far hit five boundaries and a six, while Khawaja has six boundaries to his credit.
Khawaja lived dangerously in the fourth over of the day when wicketkeeper Sarfraz Ahmed missed a stumping off Yasir with Khawaja out of his crease.
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