Port threatened a Gabba upset when they rallied to lead in the second quarter and then surged again to trail by just 10 points in the third term.
But the hosts had the answers in a 19.9 (123) to 11.9 (75) win on Saturday night.
Cam Rayner (three goals) and Hugh McCluggage (26 disposals, nine clearances, four scoring assists, one goal) starred as usual Brisbane weapon Lachie Neale was held to just a single first-quarter touch and finished with 19 in total.
Joe Daniher also kicked three of his five goals in a crucial third term run after 200-gamer Charlie Cameron had booted two in an instant in his 200th game.
Port now host GWS in a knockout semi-final while Brisbane will host the winner of Melbourne-Carlton in a preliminary final at the Gabba - they haven't lost at the ground in 12 games this season - to earn a shot at their first flag since 2003.
The Power will be rueing some errant kicking, the visitors scoring from 20 of their 48 forward entries but missing crucial set shots when the game was in the balance.
Usually reliable, Todd Marshall sprayed two of his from close-range that didn't even register, Ollie Lord the unlikely source with a season-high four goals.
Willem Drew kept Neale under control but McCluggage stepped up, his poise and positioning ensuring Brisbane's offence flowed.
Connor Rozee played that role for the Power, often emerging out the front of stoppages to slice up the Lions' much-improved defence.
The 36,020-strong crowd were still singing Cameron's trademark Country Roads goal celebration song when the small forward raced onto another chance and kicked his second in a memorable third-quarter moment.
Marshall had the reply but McCluggage stayed calm, finding Daniher with another exquisite kick forward that prompted the Lions' decisive burst.
Earlier Jason Horne-Francis imposed himself on the contest with a series of barging runs and Port finally found their radar to boot three in quick time and snatch a two-point lead.
But Rayner popped up again to steal it back with his third goal, before McCluggage and Dayne Zorko took their chances in the closing stages of the half to rebuild a 16-point advantage.
Brisbane rookie Jaspa Fletcher, who kicked a key third-quarter goal, and teammate Callum Ah Chee were both rock solid when questions were asked.
Port coach Ken Hinkley substituted Darcy Byrne-Jones to inject veteran Travis Boak with seven minutes to play.
But no sooner did Trent McKenzie and Dylan Williams hobble off with injuries, Brisbane surged clear in that time to ensure no nervous fourth-quarter moments.
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