Electing to bat, the Aussies were hurt by pacer Umesh Yadav’s (3/42) early burst that fetched him two wickets.
Yadav drew first blood after cleaning up opener Alex Doolan for 18 and soon got left-hander Phillip Hughes for 12. Mishra kept up the pressure to pack Chris Lynn (12) back to the pavilion.
Recovering from 64 for three, Peter Forrest (77) and skipper James Faulkner (94) then put on a 133-run fourth-wicket partnership to resurrect the innings.
Yadav broke the dangerous stand after getting Forrest caught behind to put the hosts in trouble at 197 for four.
Mishra (4/114) then spun into action and the veteran bowler got Faulkner caught behind as the number five batsman got his 11th first-class fifty but missed out on his maiden ton.
Brief scores: Australia A: 288/7 in 90 overs (Peter Forrest 77, James Faulkner 94; Amit Mishra 4-114).