Port threatened a number of times to blow out the margin, but the Giants were regularly able to answer, ultimately succumbing 20.12 (132) to 15.7 (97).
Five talking points: Greater Western Sydney v Port Adelaide
Jared Polec continued his break-out season for the Power, finishing with 30 touches and three goals, while Matt White, Robbie Gray, Kane Cornes and the returning Paul Stewart were all influential and Jay Schulz kicked six goals.
For the Giants, Matt Buntine did a superb job on All Australian Chad Wingard and Toby Greene managed to quell Port skipper Travis Boak in two encouraging defensive performances.
Callan Ward shook off a knock to his shoulder to tally 40 disposals, 11 marks, eight tackles and nine clearances, with Devon Smith kicking three goals and Jonathon Patton, Will Hoskin-Elliott and Rhys Palmer all kicking two.
It is Port's fourth straight win and takes its record to 6-1 ahead of next week's clash with Fremantle, while the 2-5 Giants' next task is a trip to Perth to take on West Coast.
Power coach Ken Hinkley expected a contest against the young Giants and was happy just to notch up another win.
"I've got some experience of the younger sides and I know what they're like, if they get a sniff they can keep coming," he said.
"They've got undeniable talent out there and they were pretty good and made us work to the end.
"We came up here to get a win, that's the number one thing."
The Giants started well, registering three of the game's first four goals for an early 12-point lead.
But the Power gradually set about turning the tide, with two late goals to Polec steering them to an 11-point advantage at quarter-time.
The visitors then piled on three more goals to start the second term to open up a 30-point lead and the warning signs were there for GWS, but the home side managed to steady.
The teams traded goals as Port took a 32-point lead at the main break.
With All Australian forward Jeremy Cameron shifted to full back, Patton put his stamp on the game with two third-term goals as the margin was reduced to 20 points and the 6,549 people in the stands sensed an upset.
On a bitterly cold, wet day in Canberra, the crowd was the third lowest in GWS history and its smallest to date in the nation's capital.
But the Power showed their class by responding immediately, pouring on three goals in three minutes to re-establish a 39-point lead at the final change.
The match remained a contest in the final term, with the Giants kicking six goals to five in a performance that should please coach Leon Cameron.
"They're one of the fittest sides in the competition and for us to win the last quarter, I was proud of our boys to hang in there," he said.
"As we know we're a young side and we have some brain fades that cost us goals, but I was proud of the effort."
Port's Robbie Gray continued his impressive 2014 form with 30 disposals in Canberra. Picture: AFL Media
GREATER WESTERN SYDNEY 3.4 5.4 9.6 20.12 (132)
PORT ADELAIDE 5.4 10.6 15.9 15.7 (97)
GOALS
Greater Western Sydney: Smith 3, Hoskin-Elliott 2, Palmer 2, Patton 2, Lamb, Cameron, Giles, Shiel, Scully, Kelly
Port Adelaide: Schulz 6, Monfries 3, Polec 3, White 3, Wingard 3, Gray, Impey
BEST
Greater Western Sydney: Ward, Smith, Buntine, Haynes, Hoskin-Elliott, Shiel
Port Adelaide: Polec, White, Gray, Cornes, Wines, Young, Schulz
INJURIES
Greater Western Sydney: Nil
Port Adelaide: Hartlett (flu) replaced in selected side by Paul Stewart, Carlile (flu) replaced in selected side by Newton
SUBSTITUTES
Greater Western Sydney: Jed Lamb replaced Jono O'Rourke in the third quarter
Port Adelaide: Jarman Impey replaced Tom Jonas at three-quarter time
Reports: Nil
Umpires: Fisher, Nicholls, Ryan
