Smith's unbeaten 100 from 168 balls helped Australia reach 465-6 and take a 22-run first-innings lead after lunch.
But play came to an early end because of rain just two balls after Smith, 27, brought up his fourth century of 2016.
Usman Khawaja only added two runs to his overnight 95 but Peter Handscomb made a spirited 54 alongside Smith.
With rain falling, the players went off for an early tea and play was eventually abandoned shortly before 5pm local time.
The weather looks to have ended Australia's hopes of forcing a win and wrapping up the three-match series 2-0.
Meanwhile, it has been announced that Jason Gillespie will join the Australia coaching staff as an assistant for the Twenty20 series against Sri Lanka.
The former Yorkshire coach, now with the Adelaide Strikers in the Big Bash League, will work alongside Justin Langer who will serve as the head coach.
The pair are stepping in for Darren Lehmann and his assistant David Saker as the three-match series clashes with the Test squad's tour of India.
It will be a first taste of international cricket for Gillespie, who led Yorkshire to consecutive County Championship titles before leaving at the end of the 2016 season to return to his native Australia.
"I'm just buzzing to get this role - it really is an exciting opportunity," said the 41-year-old former Test bowler, who took 259 wickets in 71 Tests and 142 wickets in 97 ODI appearances.
Captain Steve Smith struck his 17th Test century as Australia overtook Pakistan's total on a rain-hit fourth day of the second Test in Melbourne.