It secured a fifth trophy of 2025 for the French club.
Lee Kang-in scored in the 85th minute for PSG and fellow substitute Goncalo Ramos grabbed an equaliser in the fourth minute of added time to make it 2-2 in regulation on Wednesday night in Udine, Italy.
Nuno Mendes converted the clinching penalty in the shootout.
"Sometimes football is unfair," PSG coach Luis Enrique said.
"I have to say we were very lucky in the last 10 minutes that we could score two goals ... My players had faith until the last minute, like our supporters."
The Super Cup is an annual early-season match between the most recent winners of the Champions League (PSG) and Europa League (Tottenham), and it was hardly going to script when the English club took a 2-0 lead early in the second half.
Defenders popped up with Spurs' goals, with Micky van de Ven showing quick reactions to prod home the opener in the 39th minute after new PSG goalkeeper Lucas Chevalier tipped Joao Palhinha's shot onto the crossbar.
Chevalier — playing ahead of Gianluigi Donnarumma, who announced on Tuesday he was leaving PSG — might have been unlucky with the first goal but was to blame for the second after failing to keep out a header from newly appointed Tottenham captain Cristian Romero in the 48th.
PSG, who were involved in the Club World Cup until mid-July, finished strongly at Stadio Friuli, though, and hit Tottenham with late goals as Lee smashed in a low shot from the edge of the area and Ramos headed home Ousmane Dembele's right-wing cross.
In the shootout, Vitinha missed PSG's first attempt but the French team then converted four in a row. Van de Ven and Mathys Tel failed to score for Tottenham, whose manager Thomas Frank was taking charge of his first competitive match with the Premier League team.
"There are lots of things to be happy with. That needs to be the foundation going forward," the Spurs boss said.
"The single result, 2-2, is good. If you look into the performance, the shift the players put in ... wow, what a mentality."
Frank took over in the off-season following the firing of Australian Ange Postecoglou, who led Tottenham to their first trophy in 17 years with a victory over Manchester United in the Europa League final in May.
PSG completed the Champions League-Ligue 1-Coupe de France treble last season, also winning the Trophee des Champions in January. They lost the Club World Cup final to Chelsea.
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