Alastair Cook again fell cheaply and James Vince nicked off, leaving Mark Stoneman (19no) and Joe Root (5no) to battle through to stumps – England closing on 33-2, a lead of only seven.
Australia had earlier earned a useful first innings advantage, Smith showing incredible discipline to end up 141 not out as the hosts were bowled out for 328.
England began the day needing to break a partnership between Smith and Shaun Marsh that had stretched to 89 on the second evening and although Marsh (51) was able to reach his half-century, he was undone by a Stuart Broad leg-cutter soon after.
The left-hander attempted an expansive drive but was onto the shot far too early and ended up just chipping the ball to James Anderson at mid-off.
Smith and Tim Paine got through the next 13 overs until the new ball but Anderson (2-50) needed just four balls with it to remove the latter, Jonny Bairstow taking a fine one-handed catch behind the stumps.
Broad (3-49) followed that up in the next over by having Mitchell Starc caught and bowled to leave Australia 209-7 and still trailing by 93.
England will have been confident of earning a decent first innings lead but Smith showed no sign of faltering and was ably supported by Pat Cummins, the No 9 following his captain’s lead and batting with admirable patience.
The England bowlers were made to toil in the afternoon session with Anderson appearing to be nursing an injury – although England maintain their record Test wicket-taker is fully fit – and Smith reached a fine hundred, the 21st of his Test career, from 261 balls.
The breakthrough finally came when Cummins (42) edged Chris Woakes (1-67) to Alastair Cook at slip, ending an eighth-wicket stand of 66.
Still England were made to wait to wrap up the innings though as Smith stood firm and Hazlewood and then Nathan Lyon stuck around to help Australia move past England’s first innings 302 before Root (1-10) snared the final wicket.
Trailing by 26, England were soon under pressure as Hazlewood (2-11) lured Cook (7) into a hook shot that came off the top edge and was well taken by Starc, tumbling in the deep.
With the Gabba crowd as loud as they have been at any point in the match, Australia turned up the heat on England and Hazlewood squared up James Vince (2), who nicked the ball to Smith at second slip.
Root came in and was rattled by a fierce bouncer from Starc that thudded into his helmet. The England captain battled on and together with Stoneman, who endured his own short-ball onslaught from Cummins, ensured the tourists remained just two down at the close.