Smith cut Sohail Khan for three through the off-side to bring up his fourth Test hundred of the year and help build a 22-run lead over the tourists when tea was called.
He was unbeaten on 100 with Mitchell Starc not out seven in Australia's 465 for six.
The umpires took the players from the field for deteriorating light just before a storm lashed the Melbourne Cricket Ground.
The Australians lost the wickets of under-pressure pair Nic Maddinson and Matthew Wade in the middle session.
More From This Section
Under pressure after scores of 0, 1 and 4 in his three Test innings, Maddinson advanced down the wicket but failed to get to the pitch of the ball and was cleaned up.
Wicketkeeper Wade again missed out, this time he was caught in the slips off a slash outside off-stump from Sohail Khan for just nine.
Wade, like Maddinson, has struggled for runs since his recall for last month's third Test against South Africa and has scores of 4, 7, 1 not out and now 9 in his four innings this season.
Usman Khawaja was dismissed on 97 for the second time this season when he played away from his body and edged Wahab Riaz to wicketkeeper Sarfraz Ahmed.
He faced 12 balls for two runs Thursday before he was out in the day's fifth over and left the ground with his head bowed.
Khawaja also missed out on a century against South Africa in the second innings of last month's first Test in Perth.
He was dropped off a sharp caught-and-bowled chance by Mohammad Amir on 51, but three runs later he found Sami Aslam at point off Sohail.
Handscomb, playing on his home pitch, added 92 runs with Smith off 141 balls.
Paceman Riaz continued to have problems bowling no-balls and has overstepped 12 times in the 27 overs he has bowled so far.