Dockers skipper Alex Pearce took a soaring pack mark and goaled with less than a minute remaining, giving his side a precious 13.14 (92) to 13.8 (86) victory.
Freo were 14 points down early in the last quarter but booted four of the last five goals.
Freo jump from sixth to fourth ahead of games against Brisbane (home) and Western Bulldogs (away) in the run to the finals.
Fremantle withstood a massive fright from 11th-placed Port, who logged a season-best eight-goal quarter.
Port were bossed by Fremantle in the opening term as the visitors scored 4.5 to 0.4.
But the Power violently turned the tide with an unheralded second quarter of 8.1, including seven goals in a 16-minute patch.
Spearhead Mitch Georgiades scored the first major seven minutes into the term. By the 23rd minute, Port had turned a 26-point deficit into a 10-point advantage.
Georgiades added another in a spree including a Jack Lukosius stunner featuring a clever ground-ball tap, a dummy and a checkside from a tight angle.
The burst also included Aliir Aliir's first goal in 112 games for the Power. His strike after a 50m penalty gave the home side an 8.5 to 7.9 edge at halftime.
"Clearly, the second quarter was as good as we have played for some time," Port coach Ken Hinkley said.
"It was nice to actually see that from a quite a young side out there ... executing under some pressure against a side who is in the top four."
Port twice stretched their lead to 15 points in the third term.
And twice, Freo's 21-gamer Murphy Reid reduced the margin with eye-catching goals, highlighted by a remarkable bouncing effort from a boundary line.
The Power lost Lukosius to a calf injury late in the third quarter but held an eight-point buffer at three quarter-time, 11.8 to 9.12.
The home side went 14 points up when Willie Rioli goaled early in the last before Freo finished with a flourish, with Patrick Voss scoring two goals before Pearce became the unlikely match-winner.
"Mixed emotions," Dockers coach Justin Longmuir said.
"I'm really proud of the way we fought it out but we probably had our worst 20 minutes or 15 minutes of footy we have played for a long time in that second quarter."
Dockers midfielders Caleb Serong (28 touches) and Jaeger O'Meara (26) were prominent while Luke Jackson (23) was an early standout.
Voss booted three goals and his teammates Shai Bolton, Michael Frederick, Murphy Reid and Josh Treacy slotted two apiece.
Port dynamo Zak Butters collected a match-high 29 disposals and triggered the second-term onslaught, while defender Aliir was outstanding, taking 17 marks and booting his rare goal.
Power quartet Georgiades, Connor Rozee, Rioli, Jed McEntee and Lukosius all kicked two goals.
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