Smith (900 points) is placed second behind New Zealand captain Kane Williamson (919).
Win against Pakistan pushed the Kiwis to top of the heap as they became the sixth country in the past 10 years to be ranked number one in Test cricket.
The win also pushed the Black Caps firmly into contention for one of two berths in June's inaugural World Test Championship final at Lord's.
Kane Williamson becomes fastest New Zealand batsman to register 7000 Test runs
Williamson breaks Fleming's record for most 50-plus Test scores.
Kane Williamson's burgeoning 215-run stand with Henry Nicholls, who was batting on 89, helped the hosts finish Day 2 on a strong 286-3 in reply to Pakistan's first innings total of 297.
New Zealand's worst peacetime mass killing rippled through the country's top-class sports on Saturday with two high profile events cancelled and the first class cricket title being decided without a ball being bowled in the final round of matches.
Jacques Kallis, Hashim Amla, Graeme Smith, AB de Villiers, Gary Kirsten, Herschelle Gibbs, Mark Boucher, Daryl Cullinan, and Faf Du Plessis are the other Proteas batsmen who have more than 4000 runs in Test cricket.
New Zealand bundled out Pakistan on 297 in 83.5 overs.
"Our heartfelt condolences go out to the families and friends of those affected by the shocking situation in Christchurch. A joint decision between NZC and the @BCBtigers has been made to cancel the Hagley Oval Test. Again both teams and support staff groups are safe," the New Zealand cricket board tweeted on their Twitter handle.
A victory at Hagley Oval to seal a 2-0 series sweep would also push the Black Caps firmly into contention for one of two berths in June's inaugural ICC World Test Championship final at Lord's.
Home captain Williamson also praised the "special effort from" team man Wagner.
Pakistan were dismissed for 271, chasing a victory target of 372, with 4.3 overs remaining in the Test at Bay Oval.
New Zealand's late push for a place in next year's International Cricket Council's World Test Championship final will come to a head against an injury-hit Pakistan when their two-Test series begins on Saturday in Mount Maunganui.
Captain Kane Williamson returns to the side after missing the second Test
Wade will instead head to New Zealand with Australia's Twenty20 squad for a five-match series starting on Feb. 22 in Christchurch.
Ged Stokes, father of England all-rounder Ben Stokes, passed away after a year-long battle with brain cancer.
The Pakistan cricket squad was allowed to leave their managed isolation facility in Christchurch after getting clearance from New Zealand's Health Ministry on Tuesday.
Jimmy Neesham's scintillating performance with bat and a gutsy cameo by Mitchell Santner overshadowed Kieron Pollard's heroics
the PM said, "Hatred and violence have no place in diverse and democratic societies."
A jumbo Pakistan squad, led by Babar Azam, arrived in New Zealand on Tuesday and is serving a mandatory 14-day quarantine period as per COVID-19 protocol.
They will need to bat the entire final day on a deteriorating Bay Oval pitch in Mount Maunganui on Wednesday to stop the hosts taking a 1-0 lead in the two-match series.
Trent Boult needed just 15 balls to change the complexion of the second Test against Sri Lank
West Indies will play three-match T20I series before two Tests against New Zealand starting on December 3 in Hamilton. The first T20I will be played in Auckland on November 27.
"I'm probably just targeting the Test matches as usual. I've got to make sure that I'm ready for them. If I'm involved in the T20s earlier as well then that will be exciting too.'
West Indies all-rounder Rovman Powell is counting down the days until the team's two-week isolation comes to an end
The majority of the team and management arrived in New Zealand last Friday after a 54-hour flight from Barbados and have been in a biosecure facility in Christchurch.
The New Zealand government on Wednesday said that another member of the visiting Pakistan cricket team has tested positive for coronavirus, taking the total number of confirmed cases to eight.
South Africa play three ODIs against England, starting at the weekend, following on three Twenty20 Internationals.
Before they take the field for the World Test Championship final on Friday, June 18, Rajneesh Gupta takes a look at India-New Zealand Test encounters in the new century.
Rajneesh Gupta offers insights about the World Test Championship Final.
Rajasthan Royal Ben Stokes is to completely recover from jet lag after a long journey from New Zealand.
England all-rounder Ben Stokes said he had his family's blessing to return to action in the Indian Premier League with the Rajasthan Royals after taking compassionate leave to visit his father, who is ill with brain cancer.
A 16-year-old Singaporean boy, a Protestant Christian of Indian ethnicity, was detained last month under the Internal Security Act (ISA) after planning to use a machete to attack Muslims at two mosques in March, on the anniversary of New Zealand's Christchurch attacks.
Rajasthan Royals received a huge boost with premier all-rounder Ben Stokes on his way to join the team in the United Arab Emirates in the ongoing Indian Premier League.
K N Prabhu, the doyen of cricket writers, salutes Sunil Manohar Gavaskar, who appeared for the first time in Test cricket 50 years ago today, March 6, 1971.
News of all that's transpired on and off the football field
It is understood that Rajasthan Royals will 'wait' for Stokes to get back to the management and only if the cricketer confirms his availability for the second half, it will take things forward.
Earlier this month, ECB managing director Ashley Giles had said that cricketers will be provided "mental health screening" before they commit to any further tours.
He said they had caused enormous loss and hurt and stemmed from a warped and malignant ideology.
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