Virat Kohli is in danger of losing his number-one Test ranking that he has held since the Edgbaston Test against England in August.
New Zealand's last away series win against Pakistan was a 1-0 victory in matches played in Pakistan in 1969.
Kane Williamson played a masterly innings, and was 139 not out as the Kiwis reached 272-4 at the end of day four.
Yasir Shah began his 33rd Test needing five wickets to become the fastest man to reach the milestone of 200 Test wickets.
Pakistan currently trail the three-match Test series 0-1 against New Zealand.
New Zealand's narrow victory over Pakistan was the fifth smallest win in terms of runs in Test cricket history.
In his tweet, Michael Vaughan also wrote that Test cricket is "alive and kicking".
New Zealand defended a modest 176-run target, courtesy of 5-59 by left-arm spinner Ajaz Patel in his first Test.
Skipper Kane Williamson will hold the key for his team as he walked off with 27 not out and with him opener Jeet Raval on 26 not out.
Pakistan registered their 11th consecutive T20I series win after registering victory in the second match against New Zealand.
The Black Caps are scheduled to travel to the United Arab Emirates (UAE) to play Pakistan for a full tour in October-November.
Indian-born spinner Ajaz Patel was named in the New Zealand Test squad to play Pakistan in a three-match series in the United Arab Emirates in October.
England captain Joe Root and New Zealand skipper Kane Williamson are currently third and fourth in the ICC Test rankings.
SRH captain Kane Williamson backed Rashid Khan to continue his explosive Twenty20 form in Test cricket, labelling him as "the full package"
Shane Watson remained unbeaten on 117 helping Chennai Super Kings clinch their third IPL title after an 8-wicket win over SunRisers Hyderabad.
The incident was reminiscent of the 2011 World Cup final at this very venue.
IPL 2018 Final Highlights, CSK vs SRH: Chennai Super Kings beat Sunrisers Hyderabad by 8 wickets to clinch IPL 2018 title
Rashid Khan bowled a sensational spell of leg-spin, which also most won the SRH vs CSK IPL 2018 Playoff match for his side.