Promoted above Mitchell Marsh, Head was gone for 14 after Abbas drew an edge to take his fourth wicket, while the younger Marsh also failed again, making 13 before nicking a leg-break from Yasir Shah.
Azhar Ali (15) and Haris Sohail (0) were removed on consecutive deliveries by Lyon to conclude one over, and although Asad Shafiq fended off the hat-trick ball, he too went for a duck after a DRS review.
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.
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.
Fakhar Zaman (L) and Azhar Ali run between the wickets during day two of the second Test in Abu Dhabi on October 17, 2018. Tim Paine's Australia, bidding to win their first series in Asia since 2011, are unchanged from Dubai.
What are the squads for the second Test between Pakistan and Australia?
Day 2 began with Australia 20/2, 262 runs behind Pakistan.
10 - Mohammad Abbas completed 50 wickets in Test cricket in only ten matches.
The Test series against Pakistan is Australia's first since the ball-tampering scandal that erupted in South Africa earlier in the year.
Earlier, the visitors resumed their inning with 20 runs on the score board and eight wickets in hand.
"I was with the squad from the start but during the first Test I was about to return to Pakistan before, unfortunately, Imam-ul-Haq got injured and I got this chance of playing my first Test".
He was six runs from a century on debut when Labuschagne, not given a bowl until just before tea, trapped Zaman leg before wicket on the stroke of tea.
Abbas, whose first wicket of the match made him the joint second fastest Pakistani to 50 wickets, gave Pakistan an early wicket in the fourth over of the day, removing Marsh with a catch in the slip.
Fakhar and Sarfraz helped Pakistan recover from 57-5 to 282 all out after the latter elected to bat on a slow turning pitch.