Boult had out-of-form Mohammad Hafeez caught low down at second slip by Tim Southee for a fourth-ball duck.
Yasir Shah dismissed three New Zealand batsmen to come within two wickets of becoming the fastest man to 200 wickets in Tests.
New Zealand captain Kane Williamson won the toss and opted to bat in the third and final Test against Pakistan in Abu Dhabi on Monday.
Williamson said that his side are determined to move on from their crushing defeat in the second Test.
Pakistan captain Sarfraz Ahmed agreed hopes are pinned on Yasir, who has 195 wickets in 32 Tests.
Teenage pace sensation Shaheen Afridi is all set to cap his meteoric rise with a Test debut for Pakistan in the third match against New Zealand in Abu Dhabi starting on Monday.
McMillan was particularly impressed with the drift Shah got while picking the wicket of Taylor in the first innings.
Also retained is off-spinner Bilal Asif who has just five wickets to show in the last three Tests.
Yasir, who took 8-41 on Monday, had figures of 6-143 in the second innings for a match haul of 14-184.
Sohail knocked a snail-paced 147 in nine hours and 34 minutes while Azam made an unbeaten 127.