The visitors made 246 for nine. The chase begins shortly.
Hasan's previous highest score in 10 ODIs was 13, but he plastered the Black Caps bowlers to all parts in a 70-run eighth-wicket stand with Shadab.
Hasan hammered 51 off 31 balls; Shadab made 52 off 68 balls, equalling his highest against Sri Lanka in October.
Hasan, the world's No.1 bowler, normally reserves his Freddie Mercury celebrations for dismissing batsmen, but saved an encore for his batting milestone.
Outside their cameos, and Mohammad Hafeez's 60 from 71 balls, New Zealand's bowling partnerships and restrictive fielding straitjacketed the visitors early.
The hosts took advantage of a Saxton Oval pitch which struggled for bounce and carry, after being asked to field.
Six out of the eight completed ODIs at the venue have been won by the chasing team.
Pakistan's attack need to summon up their renowned guile to beat the odds.
New Zealand are looking to rustle up a ninth consecutive win across all formats.
Ten matches is the longest winning sequence in their history. The first spanned from the victory over Pakistan in January 2015 until the World Cup semifinal triumph over South Africa; the second was across all formats from the 2016 Boxing Day ODI win over Bangladesh until the result which secured the Chappell-Hadlee Trophy against Australia last February.
Trent Boult (one for 54) and Tim Southee (two for 57) were parsimonious early, restricting Pakistan to 39 for two after nine overs when Mitchell Santner was introduced.
Boult continues his supremacy in the 50-over format this season where he has 13 wickets at an average of 14.53 and strike rate of 19 across both this summer's ODI series.
Pakistan, missing form opener Fakhar Zaman who was rested with a bruised right thigh, struggled against the pressure.
Imam-ul-Haq offered a weak pull to Colin Munro at mid-wicket off Boult; Azhar Ali fell lbw to Southee for consecutive matches after stepping too far across to off stump and trying to work the ball through the legside.
On this occasion, with Pakistan 14 for two in the fifth over, he opted not to take the review, unlike the first match. Ironically, he consulted non-striker Babar Azam who could have benefited from the review at the Basin Reserve. Babar advised in the negative.
Ferguson bustled with pace, albeit on a slower surface than Wellington but he still caused havoc on occasion, defying the conditions. He coaxed the edge from Babar with his second ball, after coming on in the 11th over. Faheem Ashraf was caught by Southee at fine leg when he could not get bat to ball in time.
The spinning all-rounder duo of Mitchell Santner and Todd Astle delivered consistent returns for the most part, but Astle lapsed in his final over when he conceded 21 runs.
Captain Kane Williamson opted to use Colin Munro rather than Astle to deliver the penultimate over.
Santner finished with one for 34 from his 10 overs, including 41 dot balls; Astle took two for 50 from seven.
The concession of 12 wides will be a New Zealand concern.
