The Power outplayed and out-pressured the reigning premiers in tough, slippery conditions at AAMI Stadium and overcame a four-point three-quarter time deficit to win by three goals.
Hinkley knew what the Swans would offer in the final quarter and said ultimately he wanted the same expected of his own side.
"I said to the boys at three-quarter time, 'I can guarantee you what Sydney will do in this final quarter', we need to make sure people will say 'we can guarantee you what Port Adelaide will do'," Hinkley said.
"They'll just know there will be no carry-on, there will be a method about what we want to become.
"We'd love one day that people might like to say that Port Adelaide do it like we all talk about Sydney, the way they compete."
Hinkley said the Power beat the Swans at their own game on Saturday, praising his players' courage to remain in the contest.
He said the pressure it showed in the wet was a continuation from the previous week's 77-point hiding of Greater Western Sydney.
"Our good game last week was about our pressure … it wasn't about the scoreboard and how much we won by," he said.
"We've beaten a genuine top-four side today … they're going to be a side that's there at the end of the year.
"You want to test yourself against the best… we know how to do it and now we have to do it week-in week-out and that's what that side does."
The first-year senior coach rated the win as the best of the year and said his team was slowly becoming "more relevant" in the AFL landscape after two seasons that saw just eight wins.
"I think we're becoming a little more relevant – there's no doubt about that," he said.
"We don't give up, we fight and we fight and we keep going.
"People would sit back now at this stage and say, 'so far this playing group have lived up to what [the club's] said about them' and that is not to give up.
"Look at our badge, look at Renault, look at David Koch, we look at (CEO) Keith (Thomas), we look at the 40,000-plus members and then we look at our footy team and the footy team's been backing up all those people."
Acting captain Brad Ebert said the victory increased the respect the Power would receive from the rest of the competition.
"Being able to beat a team like Sydney does help … but we've got to keep ticking off the big teams," Ebert said.
Harry Thring is a reporter for AFL Media. Follow him on twitter: @AFL_Harry.
