Newcastle hadn't won in Melbourne since 2004, or in their last seven meetings, but they ripped up the record books to set up a grand final qualifier against the Sydney Roosters at Allianz Stadium next Saturday night.
The Knights led 18-10 with 14 minutes remaining but the Storm fought back in a thrilling finale.
Prop Jesse Bromwich barrelled across the line, and Cameron Smith added the extras to close the gap to two points.
The home side threw everything at Newcastle but couldn't find the try they needed to keep their title defence alive.
The Knights scraped into the top eight in seventh but under finals specialist coach Wayne Bennett looked worthy contenders.
They repeatedly upset the Storm's rhythm with their speed and ferocity forcing uncharacteristic errors.
The first half was played with State of Origin-like intensity, with Newcastle coming out on top 12-4.
Battle-hardened forwards Jeremy Smith, Beau Scott and Willie Mason made plenty of ground up the middle before sending the ball wide with wingers Akuila Uate and Kevin Naqiama twin dangers.
Naqiama started in place of leading tryscorer James McManus, who was a late withdrawal with an ankle injury.
Storm fullback Billy Slater gave his team the worst possible start to the second half with a school-boy error which led to a crucial try.
The Test custodian tried to catch a routine Jarrod Mullen bomb above his head AFL-style, but spilt it with Matt Hilder scooping it up to dive across the line just two minutes in.
Melbourne hit back with a try to Sisa Waqa after Kenny Bromwich batted a long ball out to the winger on the last tackle but the Knights kept a firm hold on the game.
Waqa couldn't finish the match after suffering a knee injury late in the half.
Newcastle had two tries disallowed midway through the second by the video referee, the momentum all their way until the Storm fight-back.
The home side weren't helped losing Jordan McLean with a broken jaw late in the first half after a head clash with Alex McKinnon.
Knights coach Wayne Bennett said it was a gutsy effort across the park from a team that hadn't won in Melbourne under his watch.
"I'm elated with what they did," Bennett said.
"We got ourselves in the position to win the game and we never let go.
"We can be critical of certain aspects of that last 20 minutes but the part I'm most pleased and proud of them about is that they kept Melbourne scoreless in that final 15 minutes.
"The stakes were hugely high and we didn't let them get anywhere near the tryline."
Shattered Melbourne coach Craig Bellamy paid tribute to the Knights but said his team contributed to its own demise with costly errors.
"We really contributed to our defeats the last two weeks," he said.
He said he felt his team lacked a "September buzz".
"The want, desire, the reason to believe; the last couple of weeks we haven't had that something you need in September."
The only sour note for the Knights was a knee injury to outstanding young halfback Tyrone Roberts.
He hyper-extended his knee late in the match and although played on, could miss next week's game.
NEWCASTLE 18 (M Hilder C Houston A Uate tries T Roberts 3 goals) bt MELBOURNE 16 (M Blair J Bromwich S Waqa tries C Smith 2 goals).
Referees: Gerard Sutton, Ben Cummins.
Crowd: 19,649 at AAMI Park.