It came down to a late goal to Jay Schulz - the Power's leading goal kicker - to kick the winning goal for the home side, and a trademark mark from Justin Westhoff standing tall on the defensive wing to help the victors stave off a fourth-consecutive loss.
Melbourne, gallant in defeat, played arguably their best game of losing football for the year, having seized the lead back from the Power twice during the day and looked the dominant side late in the game.
Port coughed up a five-goal lead in the second quarter to fall behind the Demons in the third term in another disappointing post-half time performance.
That term saw the Power scoreless during game time, and convert its only goal for the quarter after the siren following a high-contact free kick to Chad Wingard.
The result delivers Port Adelaide its twelfth win for the year and keeps the former league-leaders in touch with the top four.
But it wasn't a convincing result, and senior coach Ken Hinkley will use the bye weekend as part of the AFL's split round to focus his squad in the run to the home-and-away season's end.
The Power chief praised his side's ability to grind a victory away from a game of poor skills.
"I'm happy we got the win," Hinkley said after the game
"I know we didn't play great footy, but that would be really unfair to the Melbourne footy club and [Paul] Roos, because they put us under enough pressure... as we know sometimes you've got to turn it around.
"We got hold of the game, a little bit, early and they [Melbourne] scrapped their way back into it.
"We were hurting ourselves with our ball movement at times but I think the pleasing part for us, for Dom particularly, was that we got the win ... in a Dom Cassisi fashion, by getting on top in tackling and contested possession."
Hinkley praised Melbourne's pressure and ability to shut down the Power's run.
He admitted the pressure brought by the Demons contributed to Port slowing down.
"We were definitely under the cosh at times today, we were feeling the pressure.
"What happens with that is the run disappears and stops the ball movement - it's not the ball movement, it's the run, first, that disappears.
"Last year we had similar experiences [but] we've been able to get back on track [in games] a bit quicker this time, and been able to lose by small margins."
The result is a welcome relief for Port Adelaide which enjoys the benefit of an extra week off as part of the split round.
That will afford the side extra time to recuperate ahead of a challenging end to the season with matches against Collingwood (at the MCG), Sydney (Adelaide Oval), Gold Coast (Metricon), Carlton (Adelaide Oval) and Fremantle (Patersons).
"Everyone's a bit sore, and we've certainly got a lot of players going in [games] sore, not unlike every other team in the competition.
"We've got some significant injuries outside the team ... today we really missed our key backs.
"That's what we're dealing with, and we just need to get over that."
SCOREBOARD
PORT ADELAIDE 4.4 7.6 8.9 10.12 (72)
MELBOURNE 2.3 5.5 8.7 10.9 (69)
PORTADELAIDEFC.COM.AU'S BEST
R. Gray, Wines, Hartlett, Westhoff, Cornes, Lobbe
GOALS
Westhoff, Stewart, Schulz 2, Pittard, Boak, Wingard, Young
SUBSTITUTE
Ben Newton replaced Matt White at three-quarter time
INJURIES
nil
REPORTS
nil
CROWD
37,894 at the Adelaide Oval
