Lee converted the rebound after New Zealand goalkeeper Stefan Marinovic had parried Kim Bo-kyung's initial effort with just four minutes remaining.
It was unfortunate for Marinovic, one of four debutants in the starting XI, who had earlier given away and then saved Son Heung-min's first-half penalty.
Both sides saw goals disallowed before Lee's late intervention - Ji Dong-won's effort rightly ruled out for a blatant handball - while New Zealand captain Chris Wood can count himself a little unfortunate to see his strike in first-half stoppage time chalked off after he was adjudged to have committed a foul.
South Korea's Cha Du-ri, retiring from international football at the age of 34 after earning 76 caps, was given a rousing send-off when he was substituted just prior to the interval, with a video paying tribute to his career broadcast over the big screen during the break.
New Zealand's winless run now stands at 10 games, while for the hosts it was an improvement following Friday's disappointing 1-1 draw with Uzbekistan.
After a quiet opening South Korea twice went close from set-pieces, with both Kim Joo-young and Ki Sung-yueng heading off target from corners when they ought to have at least troubled Marinovic.
The visiting goalkeeper was in the thick of the action six minutes before the interval.
As Han Gyo-won chased a ball over the top, Marinovic hesitated before charging from his line and needlessly taking out the attacker, but he made amends by saving Son's resulting penalty.
Marinovic produced an even better stop two minutes later as he scrambled across his goal to claw away Ji's back-post header.
As planned, Cha was withdrawn shortly before the break to be afforded the ovation of the crowd and in the last notable action of the half Wood saw his goal perhaps harshly ruled out for a foul on Kim Young-gwon.
An emotional Cha gave a tearful speech on the pitch during the interval and his team-mates almost took the lead in the 53rd minute as Marinovic parried substitute Koo Ja-cheol's effort.
Ji did have the ball in the net midway through the half, but the officials were quick to spot his handball as he jumped to meet a corner.
Just as it seemed Marinovic would preserve a clean sheet on his maiden appearance, Lee - introduced for Son in the 64th minute - showed predatory instincts to slot home and disappoint the visitors.
‘Scoring in a World Cup is like winning the title – can you imagine millions of people celebrating something you did? It’s insane and made me very proud’: Brazil legend explains how much 2002 goal meant to him
'He already had the ability but didn’t use it because he was afraid to shoot – I said, "You’re a player who has to decide games – you have to take risks, mate"': Liverpool star was forced to become confident by team-mates
