After an even first quarter, the Power blew the game open with nine goals to one in the second term and were never troubled in winning 16.8 (104) to 9.12 (66).
It was a successful return to the Gold Coast for Hinkley, who was Guy McKenna's assistant for the past three years.
Port Adelaide now sits alongside Essendon on top of the competition and hosts West Coast at AAMI Stadium next Saturday.
The Power worked relentlessly both with and without the ball, suffocating the Suns (1-3) in close, and spreading hard when they won the ball.
Kane Cornes was also influential, turning his night around after a horrid first quarter.
He started alongside Gary Ablett and watched the Suns' skipper notch 15 disposals for the term, but was then set free by Hinkley.
He finished with 35 touches, an astonishing 33 of them uncontested.
As Cornes ran free, Dom Cassisi switched over to Ablett - a move Hinkley described as "fairly significant" - and kept him to 19 touches for the final three terms.
Jay Schulz (four goals) and Justin Westhoff (three) were a handful for the Suns' defence.
Schulz took a spectacular mark in the third quarter, jumping on to the shoulders of Sam Day to pull down a screamer.
The Power's pressure flustered a Gold Coast team that had been super competitive in the opening three rounds but got a big reality check on its home turf.
Whether it was Hinkley's intimate knowledge of the Suns or just his team's superior work-rate, it was largely one-way traffic.
They literally ran rings around Gold Coast in the second quarter.
Jake Neade's sublime snap typified the dominance as he tracked down a loose ball, sold Greg Broughton some candy, then calmly walked into an open goal as the Suns defender flew past him.
It was a poor night for the Suns, who entered the match without Harley Bennell (hamstring) and lost Joel Wilkinson (ankle) and Matthew Warnock (shoulder) with injury.
GOLD COAST 4.3 5.4 6.8 9.12 (66)
PORT ADELAIDE 3.2 12.5 15.8 16.8 (104)
Gold Coast: Thompson 2, Brennan, Matera, Harbrow, Hall, Smith, O’Meara, May
Port Adelaide: Schulz 4, Wingaard 3, Westhoff 3, Hartlett 3, Neade 2, Renouf
Gold Coast: Ablett, Thompson, Matera, O’Meara, Dixon
Port Adelaide: Hartlett, Cornes, Westhoff, Schulz, Wingaard, Wines, Cassisi
Gold Coast: Wilkinson (ankle), Warnock (shoulder), Bennell (hamstring replaced in selected side by Russell)
Port Adelaide: Nil
Gold Coast: Luke Russell was subbed on for Joel Wilkinson (ankle) in the second quarter.
Port Adelaide: Robbie Gray was subbed on for Jake Neade in the third quarter.
Umpires: Ryan, Findlay and Fisher
Official crowd: 11,332 at Metricon Stadium