In a lop-sided contest between bat and ball at the Sheikh Zayed Stadium, Azhar Ali's 87 was the lowest score by a top-five Pakistani batsman while the bottom half of their batting order did not get a chance to bat.
Shehzad, who had added 178 runs with Mohammad Hafeez to give Pakistan a flying start on Sunday, raised 169 for the second wicket with Azhar to put his team on top.
Continuing the good work, Younis (100 not out) hit his fourth century in five innings while Misbah (102 not out) struck his third successive Test hundred in a 193-run unbroken partnership.
Openers Brendon McCullum (9) and Tom Latham (5) survived seven overs to guide New Zealand to 15 at stumps on day two, with the team still needing 352 more runs just to avoid the follow-on.
Overnight batsman Shehzad stepped out to hit off-spinner Mark Craig for a six and took three runs off Tim Southee to bring up his 150, bettering his previous best of 147 against Sri Lanka at Sharjah earlier this year.
Corey Anderson finally got the breakthrough in the final over before lunch when he sent down a bouncer and Shehzad missed the line attempting a hook shot.
The ball hit the side of his helmet and the overbalancing batsman dropped his bat which hit the stump before a dazed-looking Shehzad needed to be helped off the field.
Shehzad hit 17 boundaries and a six in his 371-ball knock.
Azhar was denied a third successive Test century by a sharp-turning Ish Sodhi delivery which pitched outside leg stump, beat the bat and hit the top of the off-stump.
The India-born leg-spinner could have claimed Misbah's wicket as well but Craig could not get his hand to a skier on the first occasion and Jimmy Neesham spilled another in Sodhi's next over.
Younis, who scored 106, 103 not out, 213 and 46 in his last four innings, continued his dream run and his hundred came when Southee dropped him off McCullum at short mid-on.
Captain Misbah reached his hundred in the same over and immediately declared the innings.
Image: Younis Khan and Misbah-ul Haq of Pakistan acknowledge the crowd as they leave the field after scoring centuries during Day 2 of the first Test against New Zealand at the Sheikh Zayed stadium in Abu Dhabi.
Photograph: Warren Little/Getty Images
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Shehzad hits ton as Pakistan dominate New Zealand on Day 1