The Reds were the better side for long spells of the Group C clash on Merseyside, but it looked as though they might be punished for their failure to make their dominance count when Kylian Mbappe tucked home an undeserved equaliser seven minutes from time.
However, Roberto Firmino - who started on the bench after suffering an eye injury against Tottenham Hotspur at the weekend - fired home a stoppage-time winner to ensure that Liverpool maintained their perfect start to the season with six wins from six games across all competitions.
Daniel Sturridge and James Milner had earlier given last season's beaten finalists a two-goal lead which was quickly halved by Thomas Meunier, but the visitors can have few complaints at coming away with nothing following an underwhelming and lacklustre performance which sees them fall to a fourth successive European defeat for the first time in their history.
Sturridge's inclusion for Firmino was one of two changes for the hosts as captain Jordan Henderson also returned to the side, and the skipper was a driving force behind a bright start to the game from Jurgen Klopp's men.
PSG keeper Alphonse Areola was called into action after only six minutes when Milner exchanged passes with Mohamed Salah from a short corner before reaching the byline and drilling the ball across for Virgil van Dijk to draw the first save of the match.
Milner came close himself moments later when he found space just outside the area to drill a low strike towards the bottom corner, but Areola got down to turn his shot around the post.
PSG's star-studded attackers were struggling to get into the game and their lack of defensive discipline was playing into Liverpool's hands, with Mane forcing another stop from Areola in the 10th minute after Henderson had dispossessed Neymar to launch a counter-attack.
The visitors did begin to grow into the game as the first half wore on, and they finally threatened Alisson Becker's goal when Neymar skipped into the box before firing an effort straight at his compatriot, while Edinson Cavani could not get enough on his rebound.
It was a relatively rare sight of goal during a match in which Liverpool were the better team, though, and the hosts created another half-chance when Mane darted past Neymar on his way into the box, only to then slice his effort well off target.
The opening goal did finally arrive on the half-hour mark when Sturridge rewarded Klopp's faith in him with a firm header past Areola from Andrew Robertson's pinpoint cross, sparking a flurry of action which would see two more goals fly in during a 10-minute spell.
Both teams came close to adding to the scoring before the second goal, though, with Georginio Wijnaldum almost making it two in as many minutes for Liverpool before Mbappe fired over having bamboozled a sleeping Liverpool defence with his movement to meet a Neymar corner.
Just one minute after missing that golden chance, PSG found themselves facing a penalty courtesy of Juan Bernat's needless challenge inside the area, with the full-back dangling out a leg which sent Wijnaldum to ground.
Milner stepped up to take the spot kick, and having set a new Champions League record for assists in a single campaign last season, he got his own name on the scoresheet by tucking his penalty beyond the dive of Areola.
The two-goal cushion lasted only four minutes, though, as PSG pulled one back almost immediately through Meunier's instinctive finish into the bottom corner, although the replay showed that Cavani was offside during the buildup.
PSG may have been relieved to only go into the break with a one-goal deficit, but their performance did not improve during the second half and Liverpool were in complete control of the match for long spells.
Indeed, it looked as though Liverpool had restored their two-goal advantage shortly before the hour mark when Salah tucked home from close range, only for the goal to be disallowed after a notable delay due to a foul by Sturridge on Areola.
The Anfield crowd made their disapproval of the decision known to the officials and Areola, but those jeers almost became cheers shortly afterwards when Trent Alexander-Arnold picked out Sturridge, who this time could not steer his header beyond the keeper.
Sturridge and Salah then both failed to hit the target as Liverpool continued to control the tempo of the match, and Sadio Mane was the next to come close when he flashed a low strike right across the face of goal from a tight angle having expertly eluded the challenge of Presnel Kimpembe.
It was a perplexing performance from the usually free-scoring visitors, who played with very little urgency in the second half despite chasing the game and seriously struggled to get their prolific front three into the action.
However, it looked as though they might have done enough to force a point from their disappointing display when Neymar pounced on a misplaced pass from Salah before seeing the ball bounce off Van Dijk and into the path of Mbappe, who nestled his finish into the bottom corner with aplomb - PSG's first shot of the second half in the 83rd minute.
It was a sucker punch for Liverpool, who had avoided a similar punishment for their profligacy against Spurs at the weekend, but they almost responded with three minutes remaining of normal time as Alexander-Arnold's free kick took a deflection off the ball and clipped the outside of the post on its way behind.
Suddenly there was a very real threat of Liverpool losing a match they had dominated, though, and it took an important block from Van Dijk to deny Julian Draxler moments later after PSG had found themselves with a two-on-two scenario.
The home side did get the win they deserved, though, with Firmino - a 72nd-minute replacement for Sturridge - proving that there were no lasting effects from his eye injury when he worked space to shoot inside the box before firing a pinpoint finish into the bottom far corner.
It was a goal which sealed a sixth successive win for Liverpool for the first time since April 2014, while also inflicting a first defeat of the season on the previously-perfect PSG, who had scored 21 goals in their six wins this term prior to visiting Anfield.
Liverpool now find themselves as the early leaders of Group C, while PSG sit bottom after Red Star Belgrade and Napoli drew in the group's other game.
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Van Dijk, Gomez, Robertson; Milner, Henderson, Wijnaldum; Salah (Shaqiri 85'), Sturridge (Firmino 72'), Mane (Fabinho 93')
PSG (4-3-3): Areola; Meunier, Silva, Kimpembe, Bernat; Rabiot, Marquinhos, Di Maria (Choupo-Moting 80'); Mbappe, Cavani (Draxler 80'), Neymar