Australia's fragile top order again stuttered as the hosts slumped to 143-5 on the first day, before Smith came to the rescue with his second Test ton in what could be the series decider.
At stumps Australia were 326-6 with Smith unbeaten on 103 and Mitchell Johnson on 39, further loosening England's grip on the trophy at 2-0 down and three to play.
Having turned the first two Tests with his fiery fast bowling, Johnson was threatening to inflict more pain on the English, this time with the bat.
Johnson had hit six boundaries as he and Smith added a quickfire 59 and counting for the seventh wicket.
Australia lead the five-Test series after big wins in Brisbane and Adelaide, and can secure the Ashes with victory in Perth.
But not for the first time in the series they found themselves in early trouble with the bat after winning the toss.
Playing his 100th Test, as was his English counterpart Alastair Cook, Australian captain Michael Clarke elected to bat on a sweltering day.
Despite the pitch offering pace and bounce, there was no sideways movement and it looked a good strip to bat on, but England capitalised on poor shot-selection by the home side.
All of the Australian batsmen, bar opener Chris Rogers (11) who was run out by a direct hit from Jimmy Anderson, fell to reckless shots.
Spinner Graeme Swann (2-71), who struggled in the first two Tests, finally made an impact when he took a good catch to remove Shane Watson and then dismissed Clarke (24) and dashing opener David Warner (60) either side of lunch.
Paceman Stuart Broad (2-78) was also in the wickets and picked up Watson for 18, as well as having George Bailey caught on the boundary from a reckless hook shot.
The form woes of Watson, batting at three, continued when he chased a wide delivery from Broad and slashed it to Swann in the slips, while Clarke charged down the wicket at the spinner's second ball and picked out Cook at short mid-wicket.
Warner, who had a life when Tim Bresnan dropped a tough caught-and-bowled chance on 37 during a frenetic first session, cut Swann straight to Michael Carberry at backward point just after lunch.
However, Smith saved the day for the Australians with what was the most important innings of his career so far.
Smith put on 124 for the sixth wicket with the in-form Brad Haddin (55) before the wicketkeeper-batsman fell to a miscued pull shot from the bowling of Ben Stokes (1-52).
He had a slice of luck on 92, when he edged a ball from Stokes, but it fell just short of a frustrated Cook at first slip.
Smith immediately capitalised, hitting two boundaries later in the same over to reach triple figures.
He reached the milestone with a crisp pull through mid-wicket, a shot that netted him a number of boundaries during his innings.
For his hundred, Smith had been at the crease for 235 minutes, faced 173 balls, and hit 13 fours and two sixes.