There was a brief revival through the promising Babar Azam and Asad Shafiq, as they put on 39 before Wagner charged in to deliver a double blow in consecutive balls.
First Shafiq shaped to drive and dragged the widish ball back onto his middle stump; then debutant Mohammad Rizwan vigorously hooked his first ball straight to long leg in a bizarre entry to test batting.
Sarfraz Ahmed saw off the hat-trick opportunity and was there at stumps, on nine, with Babar unbeaten on 34, and looking good.
Southee had figures of three for 26 off his 11 overs, and Wagner had taken two for 15 off five.
New Zealand were dismissed for 271 shortly after tea today, leaving wicketkeeper BJ Watling unbeaten one shy of what would have been his 14th test 50.
They lost three for 93 in the elongated morning session, one of which was opener Raval for a conscientious 55, and only after the luckless Mohammad Amir had him dropped a second time at first slip by Aslam.
The conditions helped the seamers all day and Ross Taylor was beaten by a good ball from Sohail Khan after adding eight to his overnight score.
Henry Nicholls made an unconvincing 13 before edging Wahab to wicketkeeper Sarfraz.
Colin de Grandhomme, the first test bowling hero, played some handsome shots before departing first ball after lunch on a DRS decision, caught behind off lmran Khan for 37.
Watling battled through the middle session, adding 33 with Mitchell Santner - who fell to a brilliant low catch by Younis at second slip - and 36 for the ninth wicket with Southee, who had a tough stay in the middle.
Sohail finished with four for 99, while Imran took three for 52.
Pakistan are aiming to protect an impressive run of series victories. They have lost just one rubber of their last 11.
