The Power won 11.9 (75) to 11.6 (72) at Adelaide Oval on Friday night after Hawk captain James Sicily hit the post with a set shot with just 63 seconds remaining.
Hawthorn's season finishes while Hinkley, after his tenure was questioned during the week, takes his team to a preliminary final against Sydney at the SCG next weekend.
The victor of Saturday night's semi between GWS and Brisbane in Sydney will play Geelong at the MCG in the other preliminary final.
Scores were tied early in a frantic final term on Friday night when Hawk livewire Nick Watson kicked his third goal.
But the Power snared the next three majors in a four-minute burst for an 18-point buffer.
Hawthorn rallied again and were within five points when Sicily, with a tick over a minute left, marked and had set shot from 45 metres. A goal would have put the Hawks in front by a point but his kick scraped the goal-post, and the Power held on.
Todd Marshall (left) marked ahead of flying teammate Willie Rioli (right) in this contest. (Matt Turner/AAP PHOTOS)
Port's Mitch Georgiades kicked three goals and fellow forwards Willie Rioli and Darcy Byrne-Jones had two each.
Power midfielders Jason Horne-Francis - who left the late in the last term with a leg injury after accruing 19 possessions - and Ollie Wines (23) were influential, while Jase Burgoyne (25, one goal) was superb at halfback.
Hawk livewire Nick Watson's three goals included two in two minutes in the third term, which briefly put his side ahead, but Port kicked six goals to five thereafter.
Watson's teammates Jai Newcombe (31 possessions), Jack Scrimshaw (22) and Harry Morrison (23) were standouts but the visitors will rue their slow start, having been down 24-2 midway through the second term.
Port produced a pressure-packed opening quarter which rattled the Hawks.
Captain Connor Rozee - one of numerous Port players who received fierce criticism for lacklustre performances in their 84-point qualifying loss to Geelong - sparked the Power with the first goal of the game.
Port led 2.3 to 0.2 at quarter-time and skipped further ahead when Georgiades converted a set-shot, but the tide then turned.
Young Hawk Calsher Dear kicked the visitors' first goal in the 14th minute of the quarter and, 90 seconds later Mabior Chol added another when Port's Lachie Jones was penalised for a sling tackle.
Hawk Dylan Moore kicked another when Burgoyne, like Jones, was penalised for a sling tackle, and then gave away a 50 metre penalty for dissent, leaving the visitors just three points down.
The Power replied with two more majors to Hawthorn's one and were nine points up at halftime, 5.6 to 4.3.
Hawthorn's Watson then took centre stage with two goals in two minutes and his side hit the front for the first time since the first minute of the game.
But the Hawks held the lead for just 10 minutes as Port crept ahead 7.8 to 7.3 at three quarter-time.
Watson levelled scores early in the last term before Port created an 18-point break.
The gallant Hawks then rallied again before Sicily's late shot hit the post.
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