A Luke Garner try in the 43rd minute gave the Tigers a 12-6 lead, which was extended to 14-6 in the 58th minute with a penalty goal.
However, the Rabbitohs can't be counted out until the end with Dane Gagai scoring, before Reynolds erased the deficit with a 40m field goal — now worth two points.
Reynolds is becoming a 40m field goal specialist, having kicked two of the three since it returned to the competition.
But incredibly, Reynolds couldn't ice the game with a penalty goal or a field goal from 25m out.
It meant the game went to golden point extra time.
And with the fourth play of the first set, the Rabbitohs' Tom Burgess burst straight through the middle, running away and claiming the try.
But referee Gerard Sutton let the game play on, believing Burgess had dropped the ball, with the Tigers' Luke Brooks running 100m to score at the other end of the field.
It meant the game was over either way on the play, but the Bunker had the final decision.
There was plenty of confusion with Sutton awarding the try for the Tigers but reviewing the play.
"This is the cruellest way to lose a game," Dan Ginnane screamed on Fox League. "But Tom Burgess with a run for the ages."
And the Bunker awarded the try and the win for the Rabbitohs.
"There have been a over 100 golden point games, you will never forget how this one ended," Ginnane added.
"South Sydney, the most dramatic finish you can imagine, and it's Tom Burgess, the most unlikely of try scorers."
Corey Parker added: "It's a cruel game."
After the game, Burgess told Fox League how the match winning try took shape.
"We were trying to get field position for the drop goal and I just saw daylight in front of me," he said.
"It's a pretty good feeling. You don't get in that position too many times. I've had a few slam dunks in my time so I'm glad I got that one."
Asked if he was confident about getting the ball down, Burgess said: "You never know with the Bunker nowadays.
"I thought there was downward pressure there so I thought it was a try, so I was a bit surprised when I saw him run away and give the try to them. I was like s***. But I was glad they overturned it."
Social media was blown away by the finish.
Back in the studio, Yvonne Sampson said "It was the most unbelievable finish to an NRL game we have ever seen here. 18-14 the final score in extra-time, it was absolute chaos."
Cooper Cronk agreed he had never seen anything like that finish.
"The Wests Tigers played the perfect game to unsettle South Sydney for about 77 minutes," Cronk said. "Adam Reynolds two-point field goal was clutch. The play from Latrell Mitchell to get out of the in-goal in about the 60th minute mark set it all up.
"And look at the heartache from Michael Maguire. For half a second, Luke Brooks ran 100m and won the game."
Michael Ennis said "South Sydney had no right to win the game".
