Umar's scintillating 129 from 160 balls - the 11th century by a Pakistani on debut - made amends for a middle order wobble as the siblings piled on 176 runs for the sixth wicket to salvage Pakistan from 85 for five.
Chasing the Black Caps' first innings total of 429, Pakistan were left reeling on 307 for 8 at University Oval after Chris Martin and Shane Bond had ripped through the top of the order.
Martin (2 for 52) removed opening pair Khurram Manzoor (6) and Imran Farhat (22) in short order, before Bond claimed the consecutive scalps of Mohammad Yousuf (17), Fawad Alam (29) and Shoaib Malik (2).
Skipper Daniel Vettori made the key breakthrough to remove Kamran Akmal before Bond took the prized scalp of his brother Umar.
Vettori (2 for 64) picked up the final wicket of the third day in the third last over when he had Umar Gul trapped in front for 6.