The Power's fringe forward Francis Evans kicked three goals in the 13.16 (94) to 8.15 (63) victory on Sunday at Adelaide Oval.
Port will travel to Brisbane to play the second-placed Lions in a qualifying final.
The other qualifying final is also now locked in, with ladder leaders Collingwood to host fourth-placed Melbourne.
Richmond, led by the mercurial Dustin Martin, produced a spirited performance but will finish 13th.
Martin's equal game-high 33 disposals included seven inside 50s and a goal. Teammate Shai Bolton scored two majors and Thomson Dow (27 touches) and Jayden Short (26) were prominent.
Port's Connor Rozee (33 disposals, one goal), Zak Butters (30) and Dan Houston (27) were chief ball-winners for the home side.
Evans' scoring was complemented by two goals each from teammates Sam Powell-Pepper, Willie Rioli and Ollie Lord.
Port led by five points at quarter-time, 4.3 to 3.4, despite the Tigers having six more entries into their attacking 50m zone.
Power forward Lord kicked two goals, a return matched by Richmond's Bolton, while Martin collected 11 disposals for the term.
Martin's influence continued in a second quarter with another 11 touches as both sides added two goals each before a crowd of 39,860.
Port led by 6.7 to 5.11 at halftime with the Tigers' goalkicking inaccuracy preventing the visitors from cashing in on their territorial advantage; they registered 34 to 21 inside 50s for the half.
Those roles reversed in the third term as Port scored a wayward 2.6 from 18 inside 50s and the Tigers added 2.2 from seven entries.
The Power held a six-point buffer at three quarter-time, 8.13 to 7.13.
Neither team could score a goal in the final term until Port's Powell-Pepper struck in the 15th minute, rapidly followed by Evans' mid-air soccer for his third which effectively sealed victory.
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