Steele produced a Saturday stunner, shooting eight-under 64 at The Grange to be 14 under, with Australia's Smith (65) three shots adrift.
Australian Matt Jones is 10 under, while former world No.1 Jon Rahm (eight under) will need a low Sunday final round for victory.
Steele, a triple US PGA Tour winner, shot nine birdies, with a bogey at the par-4 11th his sole blemish.
He leads from New Zealander Danny Lee (13 under), who shot 67 to follow his first-round 64.
Mexico's Carlos Ortiz and Mito Pereira are firmly in the frame at 12 under, followed by a batch including Smith at 11 under.
The Queenslander is in contention after a second consecutive bogey-free round.
Smith landed four birdies in his initial six holes, while compatriot Jones also  enjoyed a hot streak - four birdies in a five-hole stretch.
Fellow Aussie Marc Leishman slipped in a horror patch of three bogeys in four holes - he finished six under after carding a 71.
Japan's overnight leader Jinichiro Kozuma failed to cash in on his nine-under opening round, enduring a topsy-turvy time - an eagle, three birdies and four bogeys in his 71.
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