Abbas finished with five for 33 to bowl out Australia for a paltry 145 to give Pakistan a 137-run lead in the first innings on the second day at Sheikh Zayed Stadium.
Pakistan stretched that lead to 281 as they were 144 for two at close, with Azhar Ali not out on 54 for his first half century in the series and Haris Sohail was 17 not out.
With eight wickets in hand Pakistan were in a great position to force a 1-0 lead in the two-match series after the first Test ended in a fighting draw in Dubai last week.
Pakistan's Mohammad Abbas celebrating dismissal of Australia's Shaun Marsh during their Test match at Abu Dhabi in United Arab Emirates on Wednesday — AP