Port led the majority of the match thanks to an opportunistic forward line led by the three-goal efforts of Jay Schulz and Chad Wingard.
Late goals from the pair sealed the Power's come-from-behind win.
As a victory it represents a massive turnaround for a club that went through a hellish 2012 season and has resurrected its standing as a football club in the national competition through the 'no surrender' philosophy of first-year coach Ken Hinkley.
Brad Ebert, Kane Cornes and Tom Logan dominated through the middle for the Power, while former captain Dom Cassisi kept Collingwood star Scott Pendlebury quiet all night.
Key backs Jackson Trengove and Alipate Carlile were strong on the Magpies' Ben Reid and Travis Cloke and were pivotal in setting the Power's forward thrusts.
In a remarkable game, the Power was able to hold strong in key parts and trigger several goal bursts to run away from the Magpies.
Port thundered out of the blocks in the second quarter after a low-scoring opening term.
Inspired by some hard-running across the ground from Angus Monfries, the Power kicked the opening three goals in as many minutes.
The first came from a clever entry into attack where Justin Westhoff dished the ball off to his captain Travis Boak as he ran into an open goal square.
The ball should have gone back to the middle for a routine centre bounce, but a frustrated Collingwood defender Heath Shaw wrestled Angus Monfries to the ground and conceded a free kick at the top of the goal square.
It handed Monfries a 'gimme' and put the momentum back in the Power's hands.
Jay Schulz slotted his second after a roaring screamer gave him a routine shot from 25 metres out.
But just as the Power tightened its grip on the lead, Collingwood hit back.
The Magpies kicked three in succession to close the margin back to six points, and it was only when Brad Ebert lifted his eyes to spot Chad Wingard alone in the goal square during time-on that Port was able to increase its half-time margin to two goals.
Jay Schulz flies high in the second term
The long change heralded a change in momentum.
Collingwood swamped the Power early in the third quarter by kicking the first three goals to hit the lead for the first time since the opening minutes of the game.
Dane Swan was his damaging best with two goals.
Everything was going Collingwood's way as its midfield gained the ascendency and spiked their inside 50s, but Port's defence held up strongly and made them earn every score.
The backline's durability was rewarded when Port eked out two goals through young guns Wingard and Wines.
Combined with behinds to Westhoff and Boak, and the Power was able to hold onto a meagre eight-point lead at the final break.
That lead quickly evaporated.
Dayne Beams and Travis Cloke combined for two early goals to snatch the lead back and hold a five-point advantage after as many minutes.
The momentum swung again and Port gave itself plenty of opportunity to take the lead back, but Schulz and Monfries failed to convert gettable shots.
Trailing by three points, the Power worked the ball forward to effect a stoppage 20 metres from goal. It was the freakish boot of Travis Boak that curled the ball along the ground to give the Power a three-point lead.
From then on it was all Port Adelaide.
As the Power's relentless assault on the Magpies' defence continued, the dynamic duo of Wines and Wingard lifted to the occasion and kicked two important spacers.
Port was home.
And it was Jay Schulz - the man deprived of finals for 11 years - who kicked the last.
A sweet moment for the club's heart and soul and for some 10-thousand ecstatic supporters dispersed throughout the home of football.
Port Adelaide players celebrate their 24-point win at the final siren
The Power will now meet Geelong in a semi-final at the MCG on Friday night.
Stay tuned to portadelaidefc.com.au for the latest news on ticketing and match information for Port Adelaide's Second Semi Final against Geelong.
AFL Second Elimination Final - Final Scoreboard
PORT ADELAIDE 2.4 6.6 8.9 12.15 (87)
COLLINGWOOD 1.4 4.6 7.7 9.9 (63)
GOALS
Port Adelaide: Wingard 3, Schulz 3, Boak 2, Wines 2, Westhoff, Monfries
Collingwood: Swan 3, Cloke 2, Keeffe, Macaffer, Williams, Beams
BEST
Port Adelaide: Logan, Ebert, Cornes, Jonas, Lobbe, Carlile
Collingwood: Swan, Beams, Macaffer, Sidebottom
INJURIES
Port Adelaide: Nil
Collingwood: Lynch (ankle) replaced in selected side by Elliott
SUBSTITUTES
Port Adelaide: Aaron Young replaced Sam Colquhoun in the third quarter
Collingwood: Alan Didak replaced Jamie Elliott in the third quarter
Reports: Nil
Umpires: Donlon, Dalgleish, Jeffery
Official crowd: 51,722 at the MCG
