The visitors had crumbled in the final session of the opening day, with Australia then surviving 16 overs to go to stumps on 61 for one with dangerman David Warner out for 38 to Jimmy Anderson.
Harris, under pressure after a poor series so far, resumed on 20 with nightwatchman Nathan Lyon yet to score.
Play began half an hour late after coronavirus drama in the England camp, with the team forced to undergo urgent rapid antigen tests as they were about to leave for the MCG.
All players came back negative, but two support staff and two family members tested positive and are isolating.
A member of the Channel Seven broadcast team also tested positive.
Coronavirus impacted the second Test at Adelaide with Australian captain Pat Cummins ruled out just before the start for being in close contact with a positive COVID-19 case.
When play got underway on day two in Melbourne, Lyon didn’t last long, hitting a breezy 10 before prodding at a full-length Ollie Robinson delivery that took a thick edge and carried to Jos Buttler behind the stumps.
Harris smacked an early boundary off Anderson, but was cautious, knowing he needs a big score with his place in the Australia team under threat.
He survived a review decision on 36 after being given out lbw, only for replays to show he clearly got bat to ball.
Labuschagne, the new number one Test batsman after his century in Adelaide, had a rare failure, undone by the pace of Mark Wood, edging to England captain Joe Root at slip on one in a massive moment for England.
Harris was joined by the usually reliable Smith, who had a let-off on one when Buttler got his fingertips to an inside edge off Anderson.
Smith rode his luck before Anderson was rewarded for a superb spell, bowling him for 16.
