The last wicket was that of Starc's to fall - trapped leg before wicket.
A ruthless Pakistan put Australia to the sword in Abu Dhabi, exposing the tourists' shallow batting order and marching towards an imposing target in the second Test.
But Abbas ensured Pakistan ended the day on top as he took out Usman Khawaja (3) and Peter Siddle (4), checking Australia's hopes of a straightforward follow-up to the epic draw of the first Test.
Nathan Lyon took four wickets in six deliveries to embarrass Pakistan in the morning, but newcomer Fakhar Zaman and captain Sarfraz Ahmed led the rescue with identical scores of 94 runs each before both were dismissed by part-time legspinner Marnus Labuschagne. The umpire didn't think it was an out, but Pakistan had it reviewed.
When he claimed his 50th wicket in his 10th Test on Tuesday, Abbas became the joint-second fastest to achieve the feat from Pakistan alongside the legendary Waqar Younis, Asif and Shabbir Ahmed.
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.
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Finch fought a lone hand in just his second Test but none of Travis Head, Mitch Marsh or Paine were able to go the distance.
Zaman scored almost three quarters of his runs on the offside, hitting eight fours and a six in his 198-ball knock.
Pakistan made two changes to the lineup that started in Dubai, giving Zaman and left-arm seamer Mir Hamza test debuts as replacements for Imam-ul-Haq and Wahab Riaz.
Test debutant Fakhar managed to stand firm, however, and he and Sarfraz gradually turned the tide, plundering boundaries before the end of the first session and then ploughing on towards tea.
4 - Fakhar Zaman and Sarfraz Ahmed getting out on 94 is only the 4th instance of two batsmen getting out on an identical score in the 90s in a Test inning.