Smith's 138 not out powered Australia to an imposing first innings total of 492 for nine declared on the second day as they sought a consolation win after England had already taken the series at 3-0 up.
When bad light ended play for the day, England were 32 without loss, a deficit of 460 runs. England captain Alastair Cook was 17 not out and Joe Root 13 not out.
Australia resumed well-placed on their overnight 307 for four after rain delayed today's start by three-and-a-half hours.
Smith was 66 not out and night watchman Peter Siddle 18 not out following Shane Watson's Test-best 176 yesterday.
The overcast conditions, despite the glare of floodlights, were more friendly to the bowlers, especially the seamers, than yesterday's blue skies when England debutant bowlers Chris Woakes and Simon Kerrigan struggled.
Indeed so poor was left-arm spinner Kerrigan's first day return of none for 53 in eight overs, he didn't bowl at all.
It did not take long for paceman James Anderson, who on moved past Bob Willis into second place in England's all-time list of leading Test wicket-takers, to make the breakthrough.
Anderson bowled Siddle with a superb ball that clipped the top of off stump. But when seam-bowling all-rounder Woakes dropped short, Smith pulled him for four to go to 89 -- the same score he made in the drawn third Test at Old Trafford.
However, there was no falling short of three figures for Smith today. The 24-year-old, playing the 12th Test of a career that saw him initially regarded as a leg-spinner who batted, went to his hundred in style by on-driving occasional medium-pacer Jonathan Trott for six.