Shah finished with 4-86 and left-arm paceman Rahat Ali took 3-45 as West Indies conceded a lead of 228 over Pakistan's first innings total of 452.
But despite falling 29 runs short of avoiding the follow-on, Pakistan skipper Misbah-ul-Haq did not enforce it and will bat again after tea.
West Indies added just 118 in the near two-hour session of batting on the Sheikh Zayed Stadium pitch.
Jason Holder (31) and Shannon Gabriel (13) frustrated Pakistan with a 27-run last wicket stand before Shah took the final wicket of Gabriel, caught at mid-on to end the innings.
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Resuming at 106-4, West Indies lost overnight batsman Jermaine Blackwood in the seventh over of the day when he edged Rahat to wicket-keeper Sarfraz Ahmed after scoring just eight.
Chase and nightwatchman Devendra Bishoo both escaped lbw calls but Sohail had the last laugh as he clean bowled Bishoo for 20, leaving West Indies struggling at 144-6.
Pakistan lead the three-match series 1-0 on account of their 56-run win in the first Test -- a day-night affair.