The touring side allowed their hosts to pile up 396 in their first innings before struggling to 312 for nine declared in reply.
Steve Smith, who will replace Michael Clarke as test captain after the final match of the series against England, was out for nought as the Australians slumped to 87 for five before Mitchell Marsh made 68 and Pat Cummins an unbeaten 82 to restore respectability.
Australia-born Steven Crook took three wickets for Northants after making a career-best 142 not out in the rain-disrupted tour game.
England lead the five-match Ashes series 3-1 ahead of the last game at The Oval which starts on Thursday.
(Reporting by Ed Osmond; editing by Justin Palmer)
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