South Korea are through to the last 16 of the World Cup after they came from a goal down to secure a 2-1 win at the Education City Stadium on Friday night.
The South Korean players huddled in a nervous circle to watch the final extraordinary minutes of Uruguay's clash with Ghana unfold on mobile phones.
But after Uruguay failed to add to their two-goal advantage, South Korea celebrated taking the runner-up spot in Group H behind Portugal by virtue of scoring more goals than the South Americans.
Wolves' Hwang, who missed his country's opening two matches through injury, came on as a 66th-minute substitute before he thrashed home Son's assist following a superb dribble and pass by the Tottenham forward directly from a Portugal corner.
"Before the match Son said, 'you are going to create something today, we trust you'," said Hwang.
"When Son got the ball I was convinced that he would pass it to me. It was an excellent pass and it made my job much more easier.
"It was difficult waiting for the result of the match between Uruguay and Ghana, but we proved once again that we could make it to the knockout stage.
"As a Korean citizen I am extremely proud, and I would like to thank all the Korean supporters. I am glad I can give them this present."
Portugal, whose passage to the knockout stages had already been secured, were bidding to become the first side to win all three group games at this tournament.
But following Ricardo Horta's fifth-minute strike they were guilty of taking their foot off the accelerator.
Kim Young-gwon hauled South Korea level on 27 minutes before Hwang's last-gasp winner.
Despite the defeat, Portugal still finish top of the group to avoid a possible second-round meeting with Brazil, who look likely to win Group G.
"We lost our organisation, our focus, and Korea controlled more of the game," said Portugal head coach Fernando Santos.
"Of course, our players were motivated, but we conceded a goal when they were on a counter-attack and this can happen at a major tournament.
"We are upset. We finished first of the group, but we wanted to win, and we wanted a better game in order to increase the morale of the players.
"That said, they will not be unmotivated. I trust my team, but this result serves as a warning to them."