Raiders captain Jamal Fogarty landed the match-clinching 85th minute penalty after Storm forward Trent Loiero was pinged for a high shot on Hudson Young in front of the posts..
The Storm looked set for a Magic Round victory in regulation time.
Leading 18-12, their fullback Ryan Papenhuyzen appeared to have sealed the win with a 75th-minute field goal in his 100th NRL game.
The one-point was disallowed due to Loiero being penalised while in possession for an elbow to the head of Raiders prop Joe Topine in a previous play, after referee Gerard Sutton appeared to ask the Bunker for a review.
"Our discipline probably cost us. It's a pretty hard one to take," Storm coach Craig Bellamy said.
Three minutes later Raiders fullback Kaeo Weekes scored a stunning individual try. From 50m out he raced away, chipped over Papenhuyzen, regathered and scored to send the match to golden point.
"Special," Raiders coach Ricky Stuart said of the play.
"I always want them to back their ability. He backed himself. The skill to catch the ball in those conditions was probably the most outstanding part."
The drama escalated when Storm prop Stefano Utoikamanu was penalised and sin-binned while in possession for stomping on Raiders hooker Tom Starling when his team was in front of the sticks.
It was the second time the front-rower had conceded a penalty while in possession.
"I'm not exactly sure what happened," Bellamy said.
"If he was in the wrong he needs to pick his discipline up. You show me a bloke that gives away two penalties when you've got the ball in a game. You are not looking at too many people."
After Loiero's high shot, Fogarty then stepped up to win it with a pressure penalty.
Scintillating Storm winger Sua Fa'alogo earlier shone.
The final Magic Round clash lived up to its billing as the match of the round with both sides inside the top four.
Pocket rocket Fa'alogo set up two tries, scored one and made three line breaks in a dazzling display.
The Raiders refused to relent. They had come back from an 18-point deficit to win their previous clash with the Dolphins.
They were behind 14-0 after 25 minutes against the Storm and again rallied to narrow the margin to two at halftime.
Fa'alogo's 59th-minute try restored a six-point advantage.
In the first half, Cameron Munster's left-foot kick was precision personified, allowing centre Grant Anderson to swoop.
Fa'alogo set up a try for Papenhuyzen with a play of pure audacity.The speedy winger broke down the right from 70m out and at full speed hooked an inch-perfect kick onto a flying Papenhuyzen's chest. It was Magic Round magic.
The Raiders, however, are never beaten.
Their hulking winger Savelio Tamale got the better of Fa'alogo with brute strength to score in the corner.
Raiders centre Matt Timoko was too strong and determined for three Storm defenders as he scored and it was game on at the break.
There was plenty of feeling between two rivals with a history of titanic battles. Two skirmishes between multiple players broke out before Utoikamanu and Tapine exchanged open-handed shoves, with the Storm giant penalised while in possession.
Papalii was also put on report for foul play after he gave Papenhuyzen a facial.
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