BJ Anthony missed two at the line, only for Mika Vukona to fly in for the rebound and put back lay-up to close the gap.
The Tall Blacks were forced to foul, putting Chan Hee Park on the line to convert one of two, before Penney's tying three pointer from the top of the key rimmed in and out.
The home side crashed the boards to win the inbounds with 10.9secs remaining, leading to a furious finish.
Webster's three rimmed out, with the long rebound falling to the hands of Vukona, who spun to find an open Penney in the corner.
The shooting guard swished the jumper to bring the crowd to its feet, but was ruled to have his toes on the three point line, handing the visitors a shocking 76-75 win.
The Tall Blacks came out flat in the opening quarter in the face of a much improved South Korean outfit intent on showing more activity on the defensive end.
The visitors, who looked much more comfortable after an extra couple of days in the country, forced the hosts into a number of tough, contested jump shots in building a 23-18 lead.
The Tall Blacks recorded just three assists to six turnovers in the opening stanza, and had only the accurate outside shooting Kirk Penney to thank for keeping the margin at just a two possession game.
Taejong Moon and Sekeun Oh combined off the bench for 14 first quarter points as the South Korean ball movement ratcheted up noticeably from the tour opener on Tuesday night in Wellington.
Corey Webster was busy all night, running the floor in transition and curling around multiple screens after handing the ball off at the top of the key.
Back to back buckets from Webster followed by a knock down three from the corner from Penney, gave the Tall Blacks a 30-28 lead midway through the second quarter.
Webster showed how much he has grown in the national team in recent times, affecting the game on both ends and preventing the South Koreans from doubling Penney on the outside.
He was the top scorer from a competitive first half, pouring in 12 points on 5/8 shooting and managing to bail out an offense that looked much more stagnant than it had two nights earlier.
South Korea worked the triangle inside to exploit 18-year-old centre Jack Salt, who struggled in his first stint to make the correct defensive rotations in time, and it was only a Webster three in the waning moments of the first half that gave the home team a slim 40-38 advantage at the break.
South Korea took back the lead in the opening minutes of the third quarter with a floater and fast break bucket, before Thomas Abercrombie answered with two points inside to stop the run.