The game looked over at three-quarter time, but the Power roared back late with a three-goal burst.
They then missed three more shots on goal and that was enough for the Suns, who won Friday night's game 15.8 (98) to 10.13 (73) in the humid conditions.
The Suns dealt with the late withdrawal of Jamarra Ugle-Hagan and injuries to Lachie Weller and Will Graham during the match.
Gold Coast also beat St Kilda last weekend in Darwin.
"It was terrific. Obvously going two players down in the first half was incredibly tough and we played eight quarters in pretty tough conditions," Suns coach Damien Hardwick said.
"I was really proud of the boys. We dug in deep."
Hardwick added that Ugle-Hagan had been unlucky, hurting his ankle at the end of Thursday training.
"It wouldn't have been the right thing to push him out there ... we'll be available to play hopefully next week," the coach said.
Suns captain Noah Anderson was best afield with 33 possessions and eight clearances. Power onballer Zak Butters threatened at times to tear the game apart, finishing with a match-high 35 disposals.
Gold Coast improved to 7-3, while the Power paid for a flat patch either side of halftime and inaccurate goalkicking and are now 3-7..Â
Port briefly took the lead midway through the second term, but all that did was spark Gold Coast into action.
"The second quarter, it was like two halves of a quarter - the first half, we got so much right," Port coach Josh Carr said.
"Then the 17-minute mark of the second quarter, centre bounce really hurt us and they kicked five goals straight (to halftime)."
But Carr was pleased that the Power played the game out.
The Suns unleashed a seven-goal avalanche in the second and third terms that buried the Power. Gold Coast led by 40 points at three-quarter time and the match looked over.
But when Joe Richards kicked his third goal at 19 minutes into the final quarter, Port were an unlikely chance.
Richards then hit the post and Port missed another couple of chances. Port had run out of time when Gold Coast's Jed Walter kicked his third goal with a couple of minutes left.
Suns ruckman Ned Moyle also kicked three goals.
Ugle-Hagan was ruled out on Friday with an ankle injury and Jarrod Witts took his place. After kicking the first goal of the game, Graham was forced off in the second term with concussion.
Weller also was a casualty in the second quarter because of a hamstring injury.
The Power lost Lachie Jones as well in the second term because of concussion, while talls Dante Visentini and Jordon Sweet needed treatment for facial injuries after they collided late in the third term.
Coleman Medal leader Ben King only kicked one goal, but he restricted opponent Aliir Aliir's intercept marking.
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