Known more in the international cricket circles as a potent leg spinner, the 33-year-old surpassed his previous highest 42-run score in Tests to notch up a valiant ton against the Australians when his side was reeling at 89 for 6.
After playing second fiddle to his more accomplished batting partner Babar Azam in a 105-run partnership, Yasir took charge when his countryman was out for 97.
He raced to a first-ever 50 then, supported by Mohammad Abbas, brought up his hundred off 192 balls, clattering 12 fours and kissing the turf after reaching the milestone.
He had a near-miss off the bowling of Marnus Labuschagne on 33. Steve Smith believed he caught him at slip and made a big appeal, but replays showed the ball fell just short of his fingertips. Yasir was then dropped by Labuschagne off his own bowling on 43.
Pakistan had been bowled out for 302 in reply to Australia's 589 for three declared. At stumps, hosts Australia were closing in on another massive win after Pakistan were reeling at 39-3 at stumps.