PSG, back-to-back Champions League winners, went in front in the 20th minute in Salzberg on Wednesday (Thursday AEST) through a stunning strike from Kvaratskhelia, before Brian Madjo equalised on the stroke of halftime.
Doue put the French side back in front in the 61st minute, and Europa League winners Villa were unable to pull themselves level a second time in a game refereed by Somalian Omar Abdulkadir Artan, who was unable to take part in the World Cup after he was denied entry to the US.
"We are always hungry, we want more," Doue told TNT Sports.
"After the Champions League final, I said we wanted more. We have ambitions, we're a young team, and we want to win everything again this season."
Despite many of his squad having only recently returning from the World Cup, PSG manager Luis Enrique named a formidable team, with nine starters from the side that won the Champions League final.
It took a while for PSG to find their groove, and once they did Kvaratskhelia danced through the Villa defence on more than one occasion before giving his side the lead.
Villa keeper Marco Bizot saved from Doue, but moments later Doue played a pass to Kvaratskhelia just inside the area, and the winger shimmied past defender Matty Cash before unleashing an unstoppable shot.
Madjo, making his Villa debut, had plenty of chances to equalise, but sent two headers off target, with another effort going out off the outside of the post.
Seconds before the break, the 17-year-old forward's persistence paid off.
John McGinn floated a ball towards the six-yard box and Madjo, under pressure from Willian Pacho, volleyed to the roof of the net.
Madjo, signed from Metz in January but only cleared to play last week after the Court of Arbitration for Sport upheld Villa's appeal against a FIFA ruling, became the youngest-ever UEFA Super Cup scorer with his equaliser.
Luis Enrique replaced new signing Maghnes Akliouche with Ousmane Dembele at the start of the second half, but it was Villa who created the first chance, with McGinn's shot from the edge of the area parried away by Matvey Safonov.
Doue's winner came when he raced on to a through-ball from Dembele and curled his shot into the far corner, and although the offside flag went up, a VAR check awarded the goal.
Villa, who won the Super Cup in 1982, had plenty of possession late on, but PSG put in an impressive defensive display and join AC Milan and Real Madrid as the only teams to retain the trophy.
Enrique won his 13th trophy since joining PSG in 2023, while Villa boss Unai Emery has now lost all four UEFA Super Cup appearances.
PSG, who beat Tottenham Hotspur on penalties last year, will defend the French Super Cup when they take on Lens on Sunday.
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