Ali hit 64 as Pakistan built a substantial lead over Australia in their second innings.
A darting Abbas inswinger trapped opening batsman Aaron Finch (31) plumb in front of the stumps before captain Tim Paine´s off-stump was knocked back for a duck in the same over.
Leg spinner Yasir Shah ran through the tailenders with 3-45, finishing off the match by having Jon Holland caught in the slips on three.
Abbas's first 10-wicket haul in tests made him the first pace bowler to claim 15 or more dismissals in a test series in the United Arab Emirates.
Head edged to the substitute wicketkeeper, Mohammad Rizwan, who was standing in after captain Sarfraz Ahmed went to hospital for precautionary scans when he woke up on Friday and complained of headaches.
Now boasting one of the best records in Test cricket of all time, let alone for 2018, the right-arm paceman has been tipped for glory by South African great Dale Steyn.More news: Israeli Supreme Court allows United States 'boycott' student to stay
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This is as bad a run out as you'll ever see in global cricket.
Coming to the match, batting first, Pakistan managed to score 282 in their first innings after losing five wickets for just 57 runs.
It was Australia's heaviest defeat against Pakistan, beating the 356-run hammering at this same venue four years ago.
Earlier, after the wicket of veteran batsman Mohammad Hafeez early in the innings, opener Fakhar Zaman and Ali put up a good partnership to steady the Pakistan innings.
Pakistan, who could have overtaken Sri Lanka with a 2-0 series win, remain in seventh position but have advanced from 88 to 95 points and to within two points of Sri Lanka.
That wicket saw Abbas's calendar-year record read 35 wickets at 11.74 at the time of writing.
Labuschagne, playing only his second Test, grafted his way to 43 but was dismissed second over after lunch becoming Abbas's 10th victim in the match.