Usman Khawaja, whose gritty 141 had helped Australia draw the opening test, did not bat in the second innings due to a knee injury.
Australia added 24 runs to their overnight score of 47-1 when Abbas broke through by having Travis Head (36) caught behind. The 28-year-old seamer struck again in his next over, trapping Mitchell Marsh lbw for five.
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 picked with two wickets in two overs, sending Mitchell Starc (28) and Peter Siddle (3) back to the pavilion.
Marnus Labuschagne, playing his second test, grafted his way to 43 but was dismissed shortly after lunch as he top-edged a short ball from Abbas to substitute wicketkeeper Mohammad Rizwan.
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.
South Africa's joint-highest test wicket-taker Dale Steyn was impressed.
"I see a new number 1 test bowler coming... Mohammad Abbas," the 35-year-old fast bowler said on Twitter.
Jon Holland was the last to go, caught by Haris Sohail in the slip cordon off Shah for three as Pakistan clinched their biggest test victory by runs.
The series defeat means Australia dropped from third to fifth in the International Cricket Council world rankings.
The morning session started on a sour note for both teams, with Pakistan skipper Sarfraz Ahmed taken to hospital after being struck on the helmet while batting and Khawaja ruled out with a knee injury that is likely to require surgery.
The teams next meet in a three-match Twenty20 international series which begins on Oct. 24.
(Reporting by Hardik Vyas in Bengaluru; editing by Sudipto Ganguly)
