The Power trailed at three-quarter time but Wingard triggered a late surge as Port won 10.12 (72) to 8.6 (54) at a sodden AAMI Stadium.
Port ruined the comeback game of the visitor's prized recruit Kurt Tippett, who kicked a goal in the first minute and finished with two in an ominous debut for his new club.
But in wet and windy conditions, Port kicked five goals to two in the last term to stun the Swans and climb into the top eight.
Wingard booted three goals, including two in the tense final stanza, while Port's acting captain Brad Ebert, Matthew Broadbent and veteran hard-nuts Dom Cassisi and Tom Logan revelled in the heavy going.
The Swans were superbly served by midfielders Josh Kennedy and Jarrad McVeigh and backman Nick Malceski was prominent.
But the flag fancies lost ex-skipper Adam Goodes, who was substituted at three-quarter time with an injured right knee.
The dual Brownlow medallist watched a final term in which the lead changed five times before Wingard helped to seal the Swans' fate.
The 19-year-old was instrumental in delivering first-year coach Ken Hinkley his greatest win after the Power slipped behind early as Tippett took centre stage.
Tippett took a mark just 11 seconds into his playing career as a Swan, and then converted, in an impressive come back after an 11-match suspension for his illegal 2009 contract with his former club, Adelaide.
Tippett potted another some 17 minutes later as the Swans crafted a 4.1 to 1.2 advantage by quarter-time.
But Port, in two quarters of water-logged work, snuck within four points at the last break.
The home side, inspired by Wingard, then overwhelmed the reigning premiers to bank their seventh win from 12 games this season.
Swans coach John Longmire could only praise his opposition.
"They tackled well, they used the ball well and I you come up against a team that does that consistently well over four quarters you need to be doing the same thing," he said.
The Power made the most of their turnover opportunities, booting 60 points to just three.
Port coach Ken Hinkley said such a discrepancy justified the club's method.
"Hopefully it's good method…we probably made the most of them with the conditions … but your method to force the turnovers is what you worry about," he said.
"It's not what you do with the turnover, obviously it's important for you to score, but for us it's the method to get the turnover."