A lower order fightback had earlier given the Bulls a 111-run first innings lead.
Test hopeful Harris (50no) and stylish young gun Campbell Kellaway (62no) erased the deficit under lights at the Gabba in an unbroken 122-run opening stand.
The Bulls resumed at a precarious 5-94 in reply to Victoria's 186 as wicketkeeper Jimmy Peirson (61) and No.6 Angus Lovell (60) built an 84-run sixth wicket stand.
Peirson, so often a man for a crisis or the Bulls, received support from paceman Jack Wildermuth (27).
Jimmy Peirson during his 61 for Queensland against Victoria. (Darren England/AAP PHOTOS)
It was an aggressive 57 off 70 balls by fast bowler Xavier Bartlett, batting at No.9, that enabled the hosts to post 297 and take a 111-run first innings lead.
Bartlett played several agricultural heaves and an assortment of classic cricket strokes to showcase the hard work he has put into his batting of late.
Victoria pace bowler Xavier Crone (4-68) returned his best figures in first class cricket.
The failure of Australia's top order in the thrashing by India in the first Test in Perth has provided an opportunity for batters in the domestic scene to bash down the door and convince selectors they deserve an opportunity.
Harris, who missed out in the first dig, had made 469 runs for Victoria and Australia A this summer at an average of 46.9 leading into his second innings knock.
A hefty score is what the 32-year-old needs to add to his 14 Tests. He will be aiming for a hundred when play resumes on Tuesday.
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