Chad Wingard was the game-breaker as Port triumphed 13.16 (94) to 11.10 (76).
Port banked their seventh victory from eight games - their best-ever start to a season.
WATCH: Suban cops some friendly fire
The Power trailed by five points at three-quarter time but produced a customary fast finish, which over powered the Dockers.
Wingard kept the Power in the contest with his uncanny goal-kicking before the home side sealed their victory over Fremantle with five goals to two in the final term.
Dockers coach Ross Lyon tipped his hat to the Power's ability to secure the game when it was there for the taking, but lamented his side's missed opportunities.
"I thought we clawed it back pretty well, even had some opportunities late that we muffed to be frank," Lyon said.
"Fluctuating fortunes, there were times they were in control, [times] when we were in control but the bottom line is this, when the last quarter of the game was up for grabs they dominated ground ball and it was 10 [forward 50] entries to one."
Matt White kicked the first two goals of the last quarter and utility Kane Mitchell also finished with two majors.
Port midfielders Ollie Wines (27 disposals), Robbie Gray (30 touches), Travis Boak (29 possessions) and backman Jasper Pittard were prominent.
Fremantle goalsneak Matt De Boer booted three goals, all in the first half - a return matched by versatile Zac Clarke.
And Freo onballers Nat Fyfe (34 disposals, two goals), David Mundy (31 possessions) and Lachie Neale (28 touches) were influential.
But the Dockers lost Stephen Hill to a left knee injury, the playmaker substituted early in the third quarter as his injury-troubled season continued.
WATCH: Duffield collects Wingard high
Port Adelaide coach Ken Hinkley took a trademark measured approach to his side's superb 7-1 start to the year, saying the Power had been "solid".
"We've played good footy, there's no doubt we've played strong footy right through," Hinkley said.
"No coach would sit here and tell you we've played perfect footy, we've played enough solid football that we are where we are and we deserve that right now."
PORT ADELAIDE 2.4 4.8 8.10 13.16 (94)
FREMANTLE 1.3 6.6 9.9 11.10 (76)
GOALS
Port Adelaide: Wingard 5, Mitchell, White 2, Schulz, Wines, Young, Pittard
Fremantle: Clarke 3, Suban, Fyfe 2, de Boer, Pavlich, Hill, Mayne
BEST
Port Adelaide: Wingard, Ebert, Wines, Mitchell, Gray, Trengove
Fremantle: Fyfe, Sandilands, Mundy, Mzungu, Barlow, Neale
INJURIES
Port Adelaide: Matthew Lobbe (calf) replaced in selected side by Brent Renouf
Fremantle: Nil
SUBSTITUTES
Port Adelaide: Brent Renouf replaced by Aaron Young at three-quarter time
Fremantle: Stephen Hill replaced by Clancee Pearce in the third quarter
Reports: Nil
Umpires: Rosebury, Kamolins, Harris
Official crowd: 38,234 at Adelaide Oval
