Jay Schulz booted seven goals for the Power as the home team destroyed its hapless opponent, 24.15 (159) to 7.4 (46).
Click here to read about the game's big talking points
Adding to the Lions' woes was the loss of star midfielder Pearce Hanley.
Leuenberger will have scans on his right knee and Hanley strained a hamstring.
On top of Schulz's big bag, Justin Westhoff, Matt White and debutant Sam Gray each kicked three majors.
Power captain Travis Boak (41 disposals), Kane Cornes (38 possessions) and vice-captain Brad Ebert (35 touches) were outstanding before a 36,231-strong home crowd.
The Lions had no clear winner apart from Tom Rockliff (31 disposals, 14 tackles) and Rohan Bewick, who kicked two goals.
The Lions kept pace in the first term and trailed by eight points at quarter-time in a heartening opening.
But they were then blown away as Port booted 14 goals to two in the second and third quarters.
Boak, Ebert and Cornes ruled the midfield and fed a hungry forward line, where Schulz and Westhoff were ever-present threats, taking 17 marks between them.
And when the ball hit the ground, goalsneaks White, impressive first-gamer Sam Gray, and Robbie Gray (two goals) feasted on the crumbs.
The Lions' cause was hampered by the loss of tap-man Leuenberger, who hobbled from the ground in the second term after injuring his right knee in a tangle with opponent Matthew Lobbe.
After the game Lions officials were hopeful that Leuenberger avoided damage to his anterior cruciate ligament, with scans to determine the exact nature of his injury.
Hanley limped off in the third quarter with a hamstring strain and also appears certain to miss games.
Lions coach Justin Leppitsch said his team lost faith and went into "self-preservation"mode
"There are a lot of parts that we need to coach better and there's parts the players have to take ownership of as well," he said following the game.
"Whattends to happen when the scoreboard really blows out, a bit ofself-preservation comes in, you forget all about your team structures... there is a bit of that creeping in."
Port coach Ken Hinkley described his team's performance as "brutal".
"We haven't been able to, probably in my time, be able to put together really a pretty strong four quarters of football and the boys were able to do that today," Hinkley said.
"Our defensive pressure all over the ground was pretty pleasing and we wanted tocome after them as much as we possibly could.
"The Lions had a young side out there, there's no doubt about that…[but] I love the ruthlessness about keeping on going and the preparedness to keep working.
"It was a comprehensive, brutal performance."
Below: Robbie Gray in action during Port's big win over the Lions. Picture: AFL Media
PORT ADELAIDE 4.4 10.9 18.13 24.15 (159)
BRISBANE LIONS 3.2 4.3 5.3 7.4 (46)
GOALS
Port Adelaide: Schulz 7, White, Westhoff, Sam Gray 3, Robbie Gray 2, Wines, Polec, Boak, Impey, Young, Ebert
Brisbane Lions: Bewick 2,Mayes,Brown, Clarke, Redden, Zorko
BEST
Port Adelaide: Boak, Ebert, White, Cornes, Cassisi, Schulz
Brisbane Lions: Rockliff, Redden, Moloney, Mayes, Zorko,Adcock
INJURIES
Port Adelaide: Nil
Brisbane Lions: Leuenberger (knee), Hanley (leg)
SUBSTITUTES
Port Adelaide: Jack Hombsch replaced by Aaron Young at three quarter-time
Brisbane Lions: Matthew Leuenberger replaced by Tom Cutler in the second quarter
Reports: Nil
Umpires: Donlon, Hay, McInerney
Official crowd: 36,231 at Adelaide Oval
