With the fate of the series, at 2-2, hanging on this match Williamson batted with responsibility for his 13th half-century during his 97 while Taylor scored his 27th fifty after New Zealand won the toss and batted at Sheikh Zayed Stadium.
Williamson added an invaluable 116 for the third wicket with Taylor before top-edging a sweep off leg-spinner Shahid Afridi and was caught behind.
He hit eight boundaries off 119 balls, following up his 123 in the series-levelling win on Wednesday, also in Abu Dhabi.
Tom Latham chipped in with an 18-ball 22 with four boundaries and Luke Ronchi made 16.
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Williamson also added 66 for the second wicket with Dean Brownlie (34) after New Zealand lost opener Martin Guptill for eight to paceman Mohammad Irfan who finished with 2-62.
Afridi finished with 1-33 in his ten overs.
Pakistan won the first and third matches while New Zealand took the second and fourth games.
Pakistan were forced to sit out opener Mohammad Hafeez who had a recurrence of a hamstring injury while struggling paceman Sohail Tanvir was also dropped, making way for Asad Shafiq and Zulfiqar Babar.
Vettori left for home to attend his brother's wedding.