While a record victory target of 506 never looked possible, Babar’s 168 not out ensured Pakistan, 310-4 at tea, entered the test’s final session with genuine hopes of a draw.
Babar’s big hundred was studded with 18 fours.
Mohammad Rizwan was batting on 14 at the other end with Pakistan still 196 behind target.
Earlier, Australia began the final day needing eight wickets to go 1-0 up in the three-test series.
Pakistan, on the other hand, required 314 runs in 90 overs to pull off test cricket’s greatest chase or, alternatively, bat out three sessions to force a draw.
A burgeoning third wicket stand between Babar Azam and Abdullah Shafique had kept Pakistan in the contest and the duo continued to frustrate Australia when play resumed.
Mitchell Starc and Pat Cummins could not make early inroads with the new ball and Babar greeted Mitchell Swepson with back-to-back fours when the leg spinner was introduced into the attack.
Abdullah and Babar batted together for nearly 87 overs in a spectacular rearguard before Cummins broke the 228-run stand in the penultimate over before lunch.
The Australia captain induced Abdullah into a drive and Steve Smith, who had dropped the opener on 20 on Tuesday, took a waist-high catch at slip to complete the dismissal.
Abdullah hit six fours and a six during his 305-ball vigil.
Cummins struck again after lunch when he removed Fawad Alam caught behind for nine.
Babar duly completed 150, his first in test cricket, and the celebration was muted considering the task at hand.
