After dismissing the home team today for 309, the QAS were wobbling at 4-80 before the teenage duo got into the action.
McSweeney, who made a solid first class debut for the Queensland Bulls at the Gabba in the opening Shield Shield game of the summer, led the initial fightback on the way to scoring 104 before he was the fifth batsman dismissed to have the QAS 5-175.
Hunter, coming off a fine 141 not out for the QAS in their opening 2nd XI match, then got into the act, batting sensibly despite the loss to two more quick wickets in Lachy Pfeffer (4) and Andrew Gode (0).
He combined with Matthew Kuhnemann to again resurrect the innings, reaching his second century in as many games as the QAS closed in on the Tasmanian first innings.
Earlier, former Bulls and Brisbane Heat quick Alister McDermott showed his value with figures of 3-63 from 28 overs.