As fellow contenders Nathan McSweeney, Cam Bancroft and Sam Konstas all went cheaply, Harris made 74 as the home side took a first-innings lead against India A.
Australia A were dismissed at tea on Friday for 223, giving them a 62-run lead over the tourists with two days left on a pitch that is offering the bowlers plenty.
The Test squad will be named soon after this match ends and all the interest lies in who opens the batting with Usman Khawaja.
McSweeney, the Australia A captain, was moved up the order to open with Harris, but he only made 14.
Bancroft's woes persisted when he was dismissed for three late on Thursday and Konstas was the first wicket to fall on Friday morning for the same score.
Immediately after lunch, the Indians were fuming when Harris defended a delivery from spinner Tanush Kotian and the ball deflected to first slip.
It was ruled not out and as Harris pointed to his pad, indicating there was no edge, Kotian glared at the umpire and may well face a dissent charge.
Tanush Kotian (l) thought he had dismissed Marcus Harris. (Morgan Hancock/AAP PHOTOS)
Putting a high price on his wicket, Harris faced 138 balls and hit five fours.
The opener was the seventh wicket to fall when he fended at a ball from Prasidh Krishna well outside off stump and was caught behind.
Harris, 32, has played 14 Tests, most recently the 2022 Sydney Ashes match.
Late-order resistance from Jimmy Peirson (30), Nathan McAndrew (26no) and Corey Rocchiccioli (35 from 28 balls, with three fours and two sixes) gave Australia the first-inning lead.
Michael Neser, who was injured on day one, did not bat.
Krishna took 4-50, while Mukesh Kumar claiming three wickets and fellow opening bowler Khaleel Ahmed picked up two
There were two more rain delays on day two, but Melbourne's notoriously fickle spring weather had cleared by mid-afternoon.
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