Resuming on 131-2 on Tuesday after being forced to follow-on, New Zealand still trails by 106 with Henry Nicholls not out on 31 and B.J. Watling surviving on 16.
Legspinner Yasir Shah (2-111) bowled 16 wicketless overs in the morning session, while fast bowler Hasan Ali (1-15) and Bilal Asif (1-47) who were among the wickets.
Shah took 10 wickets on the third day that included career-best 8-41 to dismiss New Zealand for just 90 in the first innings. But the leg-spinner bowled either too full or too short to challenge New Zealand in the first session on Tuesday.
Hasan provided the breakthrough when Latham (50) was contentiously adjudged caught behind soon after completing his half century.
On-field umpire Paul Reiffel thought Latham had edged Hasan and went to third umpire Ian Gould to confirm through television replays.
Spikes did appear on replay technology as the ball passed the bat when Latham played a defensive shot close to his front pad. However, the batsman walked off the field in disbelief.
This ended an 80-run third-wicket stand between Taylor and Latham, who hit four boundaries in his 158-ball knock.
Two balls later Nicholls successfully reviewed an lbw decision against him as TV replays showed Hasan's delivery would have missed the leg stump.
Taylor (82) completed his half century off 54 balls when he drove Hasan through the point boundary off the first ball of the day.
But Taylor went on the defense for a while before he played a reckless sweep, half an hour before lunch, and top edged off-spinner Asif to deep backward square leg. Taylor's half century featured seven fours and a six and came off 128 balls.
New Zealand leads the series 1-0 after narrowly winning the first test by four runs.