Although Portugal was underwhelming at Education City Stadium, it appeared a draw was the best South Korea could manage.
Elsewhere in Group H, Uruguay was coasting to a 2-0 victory over Ghana, which meant La Celeste were going to join Portugal in the next round.
But a purposeful run at the heart of the Portugal defence from Son in second-half stoppage time put Fernando Santos' men under pressure and the Tottenham forward threaded a fine pass through the legs of a defender for Hwang Hee-chan to latch onto.
Hwang confidently swept past Diogo Costa to spark bedlam among the South Korea players, substitutes and staff, while head coach Paulo Bento watched on in a sense of bewilderment in the stands after earning a red card last time out.
South Korea was then left was was then left with a tense six-minute wait for the other game to finish, and Uruguay duly failed to get the additional two goals required – it was a long wait for Son.
"It was the longest six minutes of my life I'll say, but in the huddle [on the pitch] we were really positive," Son told reporters afterwards.
"The guys were saying, 'Look, we deserve this, it's well deserved'. And I said [regardless of] what's going to happen, even if Uruguay score more goals, I'm f****** proud of this team.
"That's what I said. I'm very proud of this team and that they gave everything. I was sure we were going through and then everyone was just waiting. But it was a long six minutes."
Four years ago at the same stage of Russia 2018, South Korea and Son suffered heartbreak.
Although it beat Germany on matchday three, confirming the then-holders' elimination, a 3-0 win for Sweden over Mexico ensured South Korea did not go through to the last 16.
But that disappointment did not even cross Son's mind due to the delirium brought by the victory over Portugal.
"Of course, I think it was similar moments. We beat Germany 2-0 and if Mexico won their game, probably we go through, but this time [the outcome] was different.
"We were waiting for other results, but I didn't even think about four years ago because I was so happy, so proud. What can I say? I was really happy and really proud."
The Taeguk Warriors' fightback against Portugal was evidence of their character, and Son was keen to pay tribute to the whole squad on what was a memorable day for everyone, even those who did not play.
"We are spending more time together than with friends and family because in the camp the guys have already been here more than a month," he continued.
"I think we are really close, I'm really grateful that who didn't play obviously could be really sad, but they didn't show that disappointment.
"They gave everything on the bench, supporting us. I think this makes a huge difference to be one team [rather] than just going different ways, so I'm very happy, very grateful to lead this team and have this team."
South Korea will face Group G winner Brazil for a place in the quarter-finals.