Boak was close to being substituted off after rolling his ankle in the first quarter, but returned and starred as the Power kicked the final four goals of the game to win 14.11 (95) to 11.9 (75).
Boak finished with 28 disposals and one goal, a fair effort given the 25-year-old's ankle was so swollen he is in doubt for next Saturday's clash with St Kilda.
"He had some help to get through the game," Port coach Ken Hinkley said, adding that Boak was very close to putting on the red vest when the game was 10 minutes old.
"I've just had a look and his ankle is quite big. He'll have a bit of a challenge to come up next week."
Chad Wingard (concussion) is also in some doubt for next weekend, having been accidentally knocked out by team-mate Jay Schulz in a third-quarter marking contest.
"Chad said he was fine, he was more angry about the way he'd been playing," Hinkley said.
"He looks pretty bright and fresh at the moment."
The Power raced to a 26-point lead before Melbourne had even scored in the inaugural regular-season match in Alice Springs, but from that point on were put under extreme pressure in a bruising encounter.
With 10 minutes remaining in the match, Paul Roos' men hit the front after Christian Salem kicked the opening goal of the final quarter.
Justin Westhoff kicked consecutive clutch goals in response, with Roos left ruing the four behinds his side registered in the fourth term prior to Salem's second goal.
"They had six scoring shots and we have five in the last quarter," Roos said.
"We kicked 1.4 and they kicked 4.2 - that's the difference.
"They're on top for a reason."
Hinkley refused to get carried away with his team's seventh consecutive win and 9-1 record.
"Obviously it has us on top of the ladder. It doesn't mean a lot right now," he said.
"We know we have to play better than that, but we certainly acknowledge the improvement of the Melbourne footy club."
In what was a physical and at times heated affair, opposing ruckmen Mark Jamar and Matthew Lobbe set the tone early.
The pair grappled off the ball often in the first quarter, replays showing Jamar throwing a haymaker that failed to connect.
Off-season recruits Dom Tyson and Bernie Vince were among Melbourne's best.
Max Gawn taps the ball away from Travis Boak in the Alice Springs sunshine as Jared Polec looks on. Picture: AFL Media
MELBOURNE 2.2 7.4 10.5 11.9 (75)
PORT ADELAIDE 5.4 8.4 10.9 14.11 (95)
GOALS
Melbourne: Frawley 2, Bail 2, Pedersen 2, Tyson 2, Salem 2, Gawn,
Port Adelaide: Schulz 2, Gray 2, Westhoff 2, White, Neade, Mitchell, Young, Boak, Ebert, Polec, Wines
BEST
Melbourne: Tyson, M.Jones, N.Jones, Vince, Howe, Dunn, McDonald
Port Adelaide: Gray, Broadbent, Boak, Impey, Cornes, Westhoff
INJURIES
Melbourne: Nil
Port Adelaide: Wingard (concussion)
SUBSTITUTES
Melbourne: Jimmy Toumpas replaced Max Gawn in the third quarter
Port Adelaide: Andrew Moore replaced Chad Wingard in the third quarter
Reports: Nil
Umpires: Dalgleish, Schmitt, Foot
Official crowd: 5,655 at the Traeger Park
