Taylor was 77 not out for his 23rd fifty to help his team recover from a shaky 79-4 to close the fourth day on 167-6, having an overall lead of 177 with four wickets intact.
Mark Craig (nought) was in Taylor's company as New Zealand will seek a series-levelling win in the three-Test series on an intriguing final day.
Pakistan won the first Test by 248 runs in Abu Dhabi last week.
Pakistani spinners Zulfiqar Babar (3-60) and Yasir Shah (3-65) had jolted New Zealand but Taylor stood firm.
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Babar removed Brendon McCullum (45), Kane Williamson (11) and Jimmy Neesham (11) in another display of beguiling left-arm spin on a Dubai stadium pitch which is taking notable turn.
Yasir Shah dismissed Tom Latham (nine), Corey Anderson (nought) and BJ Watling (11).
McCullum hit six fours in his 62-ball knock and when on 39 became New Zealand's second top Test run-scorer, overhauling Martin Crowe's 5,444 runs in 77 Tests.
Taylor added 46 with Jimmy Neesham (11) and hit Babar for a boundary to complete his fifty and then added 41 for the sixth with Watling.
He has so far hit ten fours in his 93-ball knock.
Earlier, Pakistan owed their fightback to Sarfraz who hit a brilliant 112 for his third hundred -- all scored this year.
He was last man out in the second over after lunch from McCullum, hitting 16 fours in a 215-minute stay, his innings balancing the match after New Zealand looked set for a big lead.