He took a return catch to remove Azhar Ali on 15 and then dismissed Haris Sohail, Asad Shafiq, and Babar Azam all without scoring.
Abbas, who was also Player of the Series in Pakistan's previous Test series in England, said the key to his success was understanding the conditions, keeping it simple while bowling wicket to wicket, and waiting to take advantage of reverse swing.
The Australian batting order struggled against Pakistan and lost all wickets at 145.
Australia's batsmen suffered collapses of 60-10 and 0-3 in the drawn first test in Dubai, and the latest flop had an all-too-familiar feel about it.
Fakhar and Sarfraz scored 94 each and helped Pakistan recover from 57-5 to a total of 282 after winning the toss and electing to bat on a slow turning pitch at Sheikh Zayed Stadium.
Fakhar hit seven boundaries in an enterprising knock.
Azhar Ali has thrown away his wicket with one of the most baffling and embarrassing run outs in recent cricket history.
"It's just insane", former Pakistan batsman Ramiz Raja said on commentary.
Earlier, the visitors resumed their inning with 20 runs on the score board and eight wickets in hand.
Mohammad Abbas and Bilal Asif have done the major damage as they bagged five and three wickets respectively on Wednesday.
This is the two-match Test bilateral series, and the first match ended in draw at Dubai.
Australia's Marnus Labuschagne leaves after his dismissal against Pakistan on day two of the second test in Abu Dhabi.
Whereas Australia is playing with an unchanged side.
Leg-spinner Yasir Shah added insult to injury when he provided another breakthrough in shape of Mitchell March (14) and left Australia 75/5.