His 122 not out in the third Test against New Zealand was also his 29th century and his 17th unbeaten, putting him one ahead of Indian great Sachin Tendulkar as the batsman with the most unbeaten Test hundreds.
Chanderpaul now has 11,199 runs from his 153 Tests.
Border scored 11,174 runs from 156 Tests before he retired in March 1994, the same month the 39-year-old Chanderpaul made his debut.
As the West Indies and New Zealand players saluted Chanderpaul -- Denesh Ramdin described him as "a legend" and Kane Williamson said "he's class you can learn a lot from" -- Chanderpaul preferred to acknowledge Border.
"AB is a great man and scored a lot of runs against us in the past and we have a lot of fast bowlers. I'm happy to get up there. Those are great guys up there," he said.
The fifth highest scorer in Test cricket is Chanderpaul's West Indies compatriot Brian Lara who amassed 11,953, while the list is headed by the recently retired Tendulkar with a colossal 15,921 from 200 matches.
The other players in front of Chanderpaul are Australia's Ricky Ponting (13,378), India's Rahul Dravid (13,288), and South African Jacques Kallis (13,140).
However, Chanderpaul was non-committal when asked if he was determined to bridge the 754-run gap and overtake Lara.
"I'm just trying to take each game as it comes along and trying to do as well as I can," he said.
The classy Chanderpaul, whose front-on stance would not be found in any coaching manual, has blossomed since Lara's retirement in 2007.
When playing in the Lara years, Chanderpaul averaged 44.60 in 101 Tests, but in 52 Tests since he has averaged a shade under 70.
West Indies 1st innings (overnight 289-6)
K. Brathwaite c Williamson b Southee 45
K. Powell c Watling b Wagner 26
K. Edwards c Watling b Southee 6
M. Samuels c Williamson b Anderson 0
S. Chanderpaul not out 122
N. Deonarine lbw Anderson 2
D. Ramdin c Watling b Anderson 107
D. Sammy c Watling b Southee 3
S. Narine b Boult 2
V. Permaul c Fulton b Southee 20
T. Best c Watling b Sodhi 25
Extras (lb6, b2, w1) 9
Total: (all out wickets; 116.2 overs) 367
Fall of wickets: 1-41 (Powell), 2-77 (Brathwaite), 3-78 (Edwards), 4-82 (Samuels), 5-86 (Deonarine), 6-286 (Ramdin), 7-296 (Sammy), 8-307 (Narine), 9-332 (Permaul), 10-367 (Best)
Bowling: Boult 26-2-84-1 (w1), Southee 28-3-79-4, Wagner 21-4-67-1, Anderson 19-3-47-3, Williamson 5-0-17-0, Sodhi 17.2-0-65-1
New Zealand 1st innings
P. Fulton c Sammy b Narine 11
H. Rutherford c & b Sammy 10
K. Williamson lbw Narine 58
R. Taylor not out 56
B. McCullum not out 11
Extras (b6, lb2 nb 2) 10
Total (3 wickets; 64 overs) 156
Fall of wickets: 1-18 (Rutherford), 2-43 (Fulton), 3-138 (Williamson)
To bat: B. Watling, C. Anderson, I. Sodhi, T. Southee, N. Wagner, T. Boult
Bowling: Best 9-1-29-0 (1nb), Sammy 10-5-17-1 (1nb), Permaul 23-4-59-0, Narine 22-9-43-2
Toss: New Zealand
Umpires: Ian Gould (ENG), Nigel Llong (ENG)
TV umpire: Paul Reiffel (AUS)
Match referee: Roshan Mahanama (SRI)