Chasing a target of 176 at Sheikh Zayed Stadium, Pakistan reached 37 for no loss with openers Imam-ul-Haq (25) and Mohammed Hafeez (8) at the crease.
Resuming at 56 for one, New Zealand's batting pair Kane Williams and Jeet Raval looked fluent in the morning session before a sharp leg-break from Shah cleaned Williamson's stumps.
Williamson's dismissal for 37 saw Ross Taylor arrive to the crease, who smashed Shah for three boundaries in an over.
But Ali's ripping inswinger trapped Taylor (19) plumb leg before wicket, before Raval's (46) cautious knock ended when he was caught behind off the medium pacer.
Wicketkeeper batsman BJ Watling (59) and Henry Nicholls (55) rebuilt the innings with a 112-run partnership, before Shah removed both batsmen to trigger a collapse.
Another sharp leg-break off a dry pitch earned Shah his fifth wicket as Neil Wagner returned to the dressing room for a duck.
With the second new ball in hand, it took Ali three deliveries to dismiss Ish Sodhi and Trent Boult to wrap up the New Zealand innings.
The visitors led by Williamson had collapsed for 153 in their first innings but had recovered well, courtesy of Boult's four-wicket haul, to bowl out Pakistan for 227 on day two.
But Pakistan's bowling attack have again proved their worth as they close in on a 1-0 lead in the three-test series.
The second test will be played in Dubai from Nov. 24-28 before both teams return to Abu Dhabi for the final test from Dec. 3-7.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
