After being reduced to 96 for five soon after lunch, Rizwan and Salman took on the Australian bowling with a pulsating 94-run stand before Rizwan fell just before tea for 88.
At the interval, Pakistan were 199 for six with Salman on 36 and Sajid Khan seven. .
Rizwan, who had been dropped for the first Test, blasted two sixes and 10 fours off 103 balls before he fell to a legside trap set by Pat Cummins.
Rizwan top-edged a pull shot for Josh Hazlewood to take the catch at fine leg after posting the highest individual score by a Pakistan batsman of the series.
Cummins made the breakthrough as he has done often throughout the series, taking his third wicket of the innings.
Pakistan made a disastrous start after winning the toss, losing four wickets in the opening session and skipper Shan Masood shortly after lunch for 35.
It was a rousing morning session for the Australians, who are looking to send off 37-year-old opening batsman David Warner as a winner in his home city in his 112th and final Test match.
Openers Abdullah Shafique and debutant Saim Ayub were dismissed inside the first two overs.
The out-of-form Shafique fell to the second ball of Mitchell Starc's opening over, needlessly playing a loose drive and nicking a catch to Steve Smith at second slip for a duck.
Ayub, brought in for Imam-ul-Haq to make his Test debut, only lasted two balls before he fell to a Hazlewood outswinger in the next over, snapped up behind by Alex Carey.
Pakistan lurched to four for two and for a time looked to be consolidating with Babar Azam playing three glorious cover drives to the ropes before he was out on first-hour drinks for 26.
Cummins appealed vociferously for lbw but was turned down by the umpire, only to seek a review and get the verdict he sought, leaving the tourists tottering at 39 for three.
Saud Shakeel copped a nasty blow on the collarbone from a Cummins lifter and in the Australian skipper's next over he prodded a catch behind to Carey for five, leaving his side further in the mire at 47 for four.
Masood had a big moment on 32 in the second over after lunch when he was caught by Smith at second slip but it was ruled a no-ball from bowler Mitchell Marsh.
Marsh got the last laugh two overs later when Masood, on 35, again edged the medium-pacer to Smith in almost identical fashion to leave Pakistan at 96 for five.
Australia clinched the three-match series with a tense 79-run win in the second Test in Melbourne over Christmas.
