Khawaja took full toll of a controversial decision early in his innings, reaching 100 after tea on Thursday at Bellerive.
Queensland were 3-239 in the last session, with Khawaja 115 and Lachie Hearne bringing up his 50.
While Queensland are second-last on the Shield ladder and Tasmania are bottom, either side could still be in contention for the final against SA if they have a big win at Hobart.
Tasmania won the toss and threatened several times to break through the Queensland top order, but Khawaja batted superbly for his 43rd first-class hundred.
He also survived a massive shout from the Tasmanians when he appeared to edge opening bowler Gabe Bell to keeper Jake Doran.
Khawaja had only made 11 and the home side was aghast when Shawn Craig ruled not out.
The ton continued the 38-year-old's form upswing after a tough domestic Test series against India, which only featured one half-century.
Khawaja rebounded to post his highest Test score of 232 in Sri Lanka in late January to solidify his spot ahead of the June Test championship final against South Africa at Lord's and next summer's domestic Ashes series.
Test all-rounder Beau Webster had taken two wickets, removing opener Matt Renshaw for 20 and No.3 Jack Clayton.
Ben McDermott cruised to 24 but threw away his wicket when he should have dispatched a short ball from Mitch Owen to the boundary, but top-edged to Doran.
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