The Crows kicked six consecutive goals out of halftime to run away with the convincing 8.10 (58) to 4.4 (28) victory at Norwood Oval on Saturday.
In her second season with Adelaide after a trade from West Coast, Kelly claimed the Showdown Medal as best afield with 28 disposals, six clearances and a goal.
Prolific ball-winners Ebony Marinoff (31 touches, seven clearances, one goal) and Anne Hatchard (29 disposals) were also prominent.
Crows forward Yvonne Bonner and Port's Ashleigh Saint were the game's only multiple goal-kickers with two each.
The Power booted three unanswered goals in the second quarter and looked capable of causing an upset when they led by three points at the main break.
But the Crows, who were beaten in a preliminary final last year, finished full of running and proved far too strong when the game was there to be won.
"It was a great contest," Adelaide coach Matthew Clarke said.
"The margin was reasonably comfortable in the end but it didn't feel like a comfortable win.
"It was tight and tense and the pressure was on. It felt like what I think we'll see from here on in."
Making matters worse for Port, Hannah Ewings will come under scrutiny for a sling tackle on Kiera Mueller during the final quarter.
Adelaide belted the Power 63-3 in their only previous AFLW meeting last year and looked on track for another big win over their cross-town rivals early.
Kelly and Bonner kicked the only two goals of the first term, putting Adelaide up 2.3 to 0.0 at quarter-time.
But Gemma Houghton put Port on the board in the second term and two goals from Saint gave the underdogs a narrow advantage at halftime.
The Crows kicked 3.3 to 0.1 in the third quarter and pulled 36 points clear in the last before Ewings' long bomb from almost 50m found the target in the dying stages.
Erin Phillips (22 disposals), Abbey Dowerick (19) and Houghton (18) all worked tirelessly for the Power.
"There's definitely some growth in our group but post-game you're a little bit frustrated because you can always do that little bit better," Power coach Lauren Arnell said.
"But we were pleased with how we were able to challenge one of the better teams in the competition and we do think we've got the ability to do that for longer."
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