The French giants followed up a 2-0 home victory in the first leg three weeks ago with a 2-1 success in the reverse fixture at the Reale Arena on Tuesday, courtesy of two goals from star man Kylian Mbappe.
PSG's No.7 opened the scoring with his 45th Champions League goal, becoming the second-youngest player (25 years and 76 days) to reach that landmark after Lionel Messi (24 years and 257 days).
Mbappe then scored his second, as well as his third of the two-legged tie, with another ruthless finish shortly before the hour mark to put Luis Enrique's side in complete control.
PSG had blown a first-leg lead in four of their previous nine Champions League knockout ties, but they made no mistake this time around, despite conceding a late goal scored by Mikel Merino, and demonstrated a professional display in San Sebastian to keep their hopes of winning an elusive Champions League trophy alive.
One of the main talking points prior to kickoff revolved around the involvement of Mbappe, who was substituted early in both of PSG's last two matches. However, the striker - who is set to leave the club at the end of the season upon the expiration of his contract - was named in Enrique's first XI as the Spaniard made five changes from the side that drew 0-0 with Monaco in Ligue 1 last Friday.
It did not talk long for Mbappe to put his stamp on the contest, as he initially curled the game's first shot over the crossbar following a neat one-two with Fabian Ruiz on the edge of the area, before using his blistering pace to get to the byline and cut a cross back to Bradley Barcola, whose first-time effort in the six-yard box was saved by Alex Remiro from point-blank range.
Real Sociedad appeared to be puzzled by the hybrid central role taken by Ousmane Dembele in the opening exchanges as Mbappe drifted out onto the left flank, where he received the ball before netting a superb opener on the 15-minute mark.
PSG's all-time record goalscorer sprinted down the left channel inside the penalty box and cleverly turned his marker inside out before whipping a brilliant right-footed shot from a tight angle into the far corner.
The French giants almost doubled their advantage just before the half-hour mark when Barcola capitalised on some slack Sociedad defending to burst down the right and set up Mbappe, but Remiro made an excellent save with his outstretched left boot to prevent the striker's snapshot creeping in at the near post.
PSG were in cruise control and has evidently learnt lessons from the first leg, as their back four managed to outwit Sociedad's high press, while Enrique's new-look attacking system was causing all kinds of problems at the other end.
Sociedad struggled to create any clear-cut chances of their own in the first half, with their only notable effort on goal coming on the stroke of half time when Takefusa Kubo fizzed a powerful strike a few yards wide of the top corner.
While Imanol Alguacil opted against making changes at half time, Enrique decided to swap Barcola with former Mallorca midfielder Lee Kang-in, who set up Mbappe to score his and PSG's second on the night just before the hour mark.
Mbappe latched onto a lofted through-ball from Lee and raced away from Sociedad's backline from the halfway line into the hosts' penalty box, before drifting inside and coolly slotting a clever finish past Remiro at the near post.
Sociedad thought they had pulled one back in the 64th minute when substitute Ander Barrenetxea directed a downward header under Gianluigi Donnarumma, but their celebrations were cut short as the former was ruled offside following a VAR check.
Barrenetxea certainly made a difference for the hosts after coming off the bench and almost picked out Mikel Oyarzabal inside the six-yard area with a dangerous delivery across the face of goal, before Merino blasted a strike over the crossbar following a positive spell of possession.
Martin Zubimendi then fluffed his lines in front of goal as he placed an effort wide from around eight yards out, but he was given a second bite of the cherry just moments later, this time flicking a fierce volley towards Donnarumma who made himself big to make an excellent save.
Sociedad, who were roared on by a bouncing Reale Arena atmosphere throughout the contest, would not go down without a fight, and they eventually got their consolation goal in the 89th minute when Donnarumma pushed a powerful shot straight into the patch of Merino, who smashed home the rebound from close range.
PSG, who will discover their Champions League quarter-final opponents when the draw is made on March 15, return to Ligue 1 duty on Sunday when they welcome Reims to the Parc des Princes, while Real Sociedad will look to return to winning ways when travel to Granada in La Liga on Saturday.