Hinkley, who was only appointed to the top job last month, was at the helm as the Power edged out the Bulldogs 14.4 (88) to 13.9 (87) at The Oval cricket ground.
[ Related: 2013 Memberships on sale ]
After trailing by six goals in the third quarter, the Power kicked nine majors on the trot before the Dogs reclaimed the lead in a see-sawing encounter.
To top off an entertaining evening in south London, Port Adelaide's Brad Ebert kicked the winning goal from the boundary line with only 40 seconds remaining.
Former Essendon forward Angus Monfries made an impact in his first outing for the Power by booting three goals although both teams were far from full strength.
Port Adelaide snatched the lead for the first time early in the last term, as what started as an afternoon game in sunshine became a clash under lights.
Monfries' third goal stretched Port Adelaide's lead to 14 points.
The Bulldogs then broke the Power surge and reclaimed the run of play, with four consecutive goals of their own to take a 10-point lead.
The counter-attack saw Higgins, Veszpremi and Picken add to their goal tallies, while Tom Liberatore booted his first.
But Port answered the challenge, with consecutive late goals - including the clincher to Ebert from a mark and set shot near the boundary.
His cool kick put the Power in front with seconds to go, allowing the Port Adelaide to hold on to a memorable win.
Hinkley was happy for his young players to be on the right side of a scoreline following a forgettable season.
"I said to the players beforehand 'you always want to win', it does not matter if it is an exhibition match or anything for us," he said.
"We are a club that needs to learn to win a bit."
Hinkley was an assistant coach at Geelong and the Gold Coast before finally being handed the reins at a club for the first time last month.
"I don't like losing and that is what most of us are about if we are in this game, we like to play to win and we were lucky enough to end up just in front tonight," he said.
"I am not sure whether we knew what we were doing, we have been together for three seconds but the coaching staff told me all along there was some talent here to work with and it is nice to see that."
