Ali was unbeaten on 52 and Asad Shafiq five not out as Pakistan reached 114-1 at stumps, increasing their lead to 342 after dismissing West Indies for 224 in their first innings.
That had given Pakistan a first innings lead of 228 and left them firmly in control as they look to claim an unassailable 2-0 lead in the three-match series.
Pakistan won the first Test -- a day-night affair played with a pink ball -- by 56 runs to take a 1-0 advantage.
Gough has now seen four of his decisions overturned in the match with fellow English umpire Richard Illingworth forced to change his initial verdict three times.
Aslam was finally dismissed when he was caught behind off paceman Shannon Gabriel for 50, although only after West Indian captain Jason Holder called for a review.
Pakistan will look to stretch their lead even further to leave the West Indies up against it on a wearing fourth and fifth day pitch at Sheikd Zayed Stadium.
"We are in a commanding position," said Shah. "We know the pitch will help spinners from tomorrow onwards so if we get a lead of 500 then we can press for a win.
"It was good to get four wickets but I was facing a bit of difficulty after bowling with the pink ball in the first Test and then switching to red here."
Resuming at 106-4, West Indies lost overnight batsman Jermaine Blackwood in the seventh over of the day when he edged Rahat Ali to wicket-keeper Sarfraz Ahmed after scoring just eight.
Chase and nightwatchman Devendra Bishoo both survived lbw appeals but Sohail had the last laugh as he clean bowled Bishoo for 20, leaving West Indies struggling at 144-6. The third and final Test will be played in Sharjah from October 30-November 3.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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