Skipper Babar Azam survived dropped catches off successive balls from Australian spinner Mitchell Swepson Wednesday to keep Pakistan in with a chance of a fighting draw on the fifth and final day of the second Test in Karachi.

Set a daunting 506-run target, Pakistan were 310-4 at tea, with Azam on a career-best 168 and Mohammad Rizwan 14, defying the Australian attack for a stubborn 33-run fifth-wicket stand.

The home team need another 196 runs for an unlikely win, or bat out a maximum of 36 overs for a hard-fought draw, as the Test headed for a nervy finale.

No team has ever scored more than 418 in the fourth innings to win a Test, while Pakistan's highest successful chase was 377 against Sri Lanka at Pallekele in 2015.

Australia dismissed Abdullah Shafique (96) and Fawad Alam (nine) in the first two sessions and could have had Azam on 161, but first Travis Head and then Marnus Labuschagne dropped sharp catches off Swepson.

Azam also survived a confident leg-before appeal against spinner Nathan Lyon when on 157, but it turned out to be umpire Aleem Dar's call on review. 

Azam has so far batted for 507 minutes and hit 18 boundaries, improving on the 143 he scored against Bangladesh in Rawalpindi two years ago.

Australia skipper Pat Cummins struck eight minutes before lunch to end an epic third-wicket stand of 228 between Shafique and Azam with the score on 249.

Shafique, who hit 136 not out in the drawn first Test in Rawalpindi, drove Cummins for a boundary to reach 96. 

But in his next over the Australian fast bowler drew the right-hander into another drive which this time found the edge.

Steve Smith held a sharp catch in the slips, making amends for dropping the same batsman, on 20, from a more straightforward chance at slip off Cummins the day before.

Cummins, who has figures of 2-56, then forced an edge off Fawad Alam to raise hopes of a victory, before the Azam-Rizwan stand halted the tourists' progress.

Australia are on their first tour of Pakistan since 1998, having previously refused to tour the country over security fears.

The third and final Test starts in Lahore on Monday.