The doubles pair of Nam Ji-Sung and Song Ming-Kyu began the fightback as they battled past Sander Gille and Joran Vliegen 7-6(3) 7-6(5) before Kwon Soon-Woo levelled the tie at 2-2 by getting past David Goffin 3-6 6-1 6-3.
World number 240 Hong Seong-Chan then sealed the tie with a 6-3 7-6(4) win over Zizou Bergs in the deciding fifth rubber in Seoul. It was the first time they had come back from losing their opening two matches to prevail.
"I'm so grateful and proud of the players for not giving up and doing their best until the end," Park said. "It's so good that I don't know how to express it.
"The players made history as a team with the coaching staff. It's like a dream to advance to the finals for two consecutive years. I don't know if this is real."
Hong, who lost his opening singles match to Goffin after Kwon fell in the first rubber, said he set out to frustrate Bergs, who is ranked more than 120 places above him.
"As soon as I started, I thought it was working well," Hong said. "The atmosphere was good before the game. Of course, I was nervous, but I was also very excited. After the match point, I thought I showed it."
A busy weekend of ties had 24 nations competing to reach the group stage to be held at four venues from September 12th-17th, with 12 winners joining 2022 champions Canada, runners-up Australia and wildcards Spain and Italy.
Finland sealed their first berth in the group stage with a 3-1 win over 2016 champions Argentina. Croatia, Chile, the Netherlands and the Czech Republic also advanced on Sunday.
List of qualifiers:
Canada, Australia, Italy, Spain, Chile, Croatia, the Czech Republic, Finland, France, Britain, South Korea, the Netherlands, Serbia, Sweden, Switzerland, the United States.
