Pakistan stand-in captain Asad Shafiq outsmarted Finch's tactic of standing well outside his crease while facing Abbas, by making Rizwan stand close to the stumps, forcing the batsman inside the crease.
After being set a target of 538, Australia could only manage 164-9 as opener Usman Khawaja did not bat after suffering a knee injury on Thursday.
Sarfraz said both teams were missing experienced players, with Pakistan's Test unit in a transition phase after last year's retirement of senior batsmen Younis Khan and Misbah-ul-Haq.
The first Test ended in a draw in Dubai last week.
Abbas had jolted Australia with four wickets off just 23 balls while Yasir Shah finished with 3-45 to give Pakistan their tenth series win on the neutral venues of United Arab Emirates. Definite positives from this series.
"It's bitterly disappointing, no doubt", skipper Tim Paine said.
"He (Abbas) challenged our defence and was too good for us". Babar Azam missed a maiden hundred by one run but he and Sarfraz Ahmed (81) put on a 133-run partnership for the sixth wicket.
Meanwhile, Mitchell Starc chased after the Kookaburra - which had actually stopped a few centimetres short of the boundary - and lobbed a throw into wicketkeeper Tim Paine, who whipped the bails off while Ali and Shafiq looked on with confusion.
Australia had reached 155-7 at lunch with the writing very much on the wall.
They have slipped from third to fifth position in the MRF Tyres ICC Test Team Rankings after losing their two-match series to Pakistan by a 1-0 margin.
Ali, who had a bad outing in the first innings was playing well in the second innings and had scored 64 before a brain-fade moment stole the grit away from his knock.