The Dockers blitzed the Power in the first half on Sunday but then flattered the hosts with a lacklustre second half to win by only 27 points, 11.9 (75) to 6.12 (48).
Skipper Matthew Pavlich kicked two goals along with Chris Mayne and Clancee Pearce as they picked up their 10th win of the season to maintain touch with the top eight.
"We're a work in progress but at 10-7 we're alive ... there's some really good signs for us," Lyon said.
"We've beat the teams around us or below us, now we need to beat somebody above us to legitimise what we're trying to do."
Nathan Fyfe was also among Fremantle's best despite returning from a lengthy stint on the sidelines after shoulder surgery in May.
The livewire had 26 disposals and took four marks with Lyon describing him as a "monster athlete" and a good winner of contested balls.
Pearce also had 22 possessions while Pavlich was quiet early but finished with 18 disposals and seven marks.
The Power's performance was dismal in the first half, the home side managing just 1.2 in what coach Matthew Primus described as the team's worst display of the season as senior players made simple skill errors.
The side showed more intensity in the opening minutes of the third quarter but still failed to put scoreboard pressure on the Dockers, who added 3.3.
Only four goals, from nine scoring shots, in the final term added some respectability for the home side.
Brett Ebert tried hard up forward kicking two goals while Brad Ebert was also effective along with Travis Boak, Andrew Moore and Kane Cornes, who finished with a game-high 31 possessions.
"Their pressure was very good but nothing that we hadn't talked about," Primus said.
"We knew it was coming.
"But to their credit they were a lot better than us in the first half and the game was done and dusted by then."
With four wins in July, the Dockers will go into Saturday's Perth derby against West Coast with renewed confidence, while Port Adelaide will look to rebound against Greater Western Sydney.