Maher mixed patience with slick strokemaking as Queensland charged to 285 for four on an uncharacteristically low, slow Brisbane wicket.
New South Wales, needing outright points to keep their final hopes alive, toiled manfully, using eight bowlers in the energy-sapping conditions.
Maher, whose innings included 16 boundaries, was overlooked by Australian selectors and it was a timely effort after Simon Katich, Brad Haddin and Mike Hussey were preferred for call-ups to the Australian One-day side this season. Paceman Stuart Clark with 2-39 from 19 overs was the pick of the New South Wales attack.
In Adelaide, opener Matthew Elliott scored his third century of the season to give top-placed Victoria the upper hand on day one of their Sheffield Shield match against South Australia at the Adelaide Oval.
Despite an impressive haul by South Australian paceman Paul Rofe, who took 4-57, including three wickets in five overs with the second new ball late in the day, Victoria managed 310 for five at stumps on the first day.
Elliott's century came from 218 balls with 10 boundaries. He was supported by fellow opener Matthew Mott who finished with 53, although the pair took 41 overs to build a century-opening stand.
Later in the day Elliott opened up, with he and Brad Hodge sharing a 134-run second wicket partnership at better than four per over before he was eventually out lbw to part-time medium pacer Mark Cosgrove.
Hodge also continued his brilliant recent form, scoring 81 from 116 balls, with 12 fours, including consecutive boundaries from off-spinner John Davison to bring up his half-century. He looked to be headed for a century before Rofe trapped him lbw with his first over with the second new ball late in the day.
Waugh brothers fail in NSW's victory bid