Shah took eight first-innings wickets for 41 and added two more after New Zealand were forced to follow on, becoming the first bowler to take 10 wickets in a day since Indian Anil Kumble in 1999.
New Zealand at least showed some fight in their second innings, managing to get to 131 for two to trail Pakistan by 197 runs at stumps and keep the faintest glimmer of hope alive.
New Zealand lead the three-test series 1-0.
Six batsmen made ducks in the first innings, equalling an unwanted test record as New Zealand collapsed to 90 all out in reply to Pakistan's 418 for five declared.
New Zealand had reached 50 without loss before the veteran Shah took centre stage to devastating effect.
That three-wicket maiden was a harbinger of worse to come for the Kiwis, and by the time Shah finished scything his way through their batting order, New Zealand had made their lowest-ever total under captain Kane Williamson.
Williamson was the sole beacon of hope for New Zealand in that woeful first innings, staying doggedly at the crease while wickets fell all around him and ending on 28 not out.
Shah continued to make inroads when the Kiwis returned for their second innings.
The 32-year-old struck early to have opener Jeet Raval stumped for just two and Williamson caught behind for 30, before Taylor and Latham steadied the ship with a 65-run partnership for the third wicket.
New Zealand won the opening test in Abu Dhabi by four runs. The teams will return to the same venue for the final match from Dec. 3-7. (Reporting by Simon Jennings in Bengaluru Editing by Keith Weir)
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