Younis Khan and Azhar Ali featured in a century-plus stand to prop up Pakistan but New Zealand claimed three wickets in the final session to stay ahead in the second Test in Dubai.
Resuming on 34 for two, Pakistan enjoyed a smooth morning session but lost Younis (72) after lunch and Azhar (75) and two other batsmen after tea to finish day two on 281 for six, still 122 runs behind the tourists.
Sarfraz Ahmed (28) and Yasir Shah (one) were in the middle at stumps with Pakistan, who lead the three-match series 1-0, still trailing New Zealand by 122 runs with four wickets in hand.
After cheaply removing Pakistan's openers late on Tuesday, New Zealand needed early wickets to take the upper hand but were thwarted by Younis and Azhar, who negotiated pace bowlers with aplomb and used their feet effectively against spinners.
Younis, who turns 37 later this month, was the more aggressive of the two, hitting off-spinner Mark Craig for two sixes - one over long on and the other over midwicket.
After dominating his 113-run third wicket stand with Azhar, Younis was dismissed by Jimmy Neesham, having extended the red hot form that had produced three centuries and a double hundred in his last six Test innings.
Sodhi was the pick of the New Zealand bowlers with two wickets for 65 runs.
New Zealand 403 all out (Latham 137, Babar 4-137)
Pakistan 281-6 (Younis 72, Sodhi 2-65)