Love knocked up his second century of the season but was bowled by Tasmanian paceman Gerard Denton without adding to his even 100 on Wednesday.
Former Test batsman Stuart Law, who has not made a century in Sheffield Shield cricket since March, 2001, came agonisingly close to breaking the drought before being caught at mid-off by Michael Di Venuto off left-arm finger spinner Xavier Doherty.
His partnership with Love added 190 runs to the Queensland tally.
Tasmania won the toss and sent Queensland into bat, taking 31 for four in the final session with two wickets to paceman Damien Wrigh who finished the day with 3-65 off 22 oversAt stumps Wade Seccombe was unbeaten on 11 and Ashley Noffke was not out 19.
Victoria's match against SA rescheduled