Juan Bernat opened the scoring with a low finish before Neymar doubled the lead, only for James Milner to give Liverpool hope with a penalty seconds before the break.
PSG had half a chance within the opening minute when Edinson Cavanbi failed to control a long ball which, had he been able to gather it in, would have left him clean through.
Their high-tempo start continued as Marco Verratti and Angel Di Maria combined to find Kylian Mbappe, whose effort deflected off Virgil van Dijk.
Before the 10-minute mark had arrived, PSG fashioned another chance after a Liverpool corner had been cleared when Di Maria's effort from distance parried by Allisson.
Neymar and Mbappe then linked, the former fouled by Milner but the referee playing advantage before the latter's low strike was saved.
But PSG didn't have to wait long before their breakthrough arrived, Bernat steering past the stranded Alisson from 10 yards after the ball had been prodded away from Mbappe.
With Liverpool struggling to find momentum and the home side sweeping forward, Georginho Wijnaldum went into the book for fouling Mbappe, Neymar's free kick then just eluding Marquinhos.
Milner cut the ball back for Mohamed Salah on the edge of the area as Liverpool looked for a response, but his effort drifted wide.
After 24 minutes, Verratti went into the book for a bad challenge on Joe Gomez before, with the half-hour approaching, Liverpool created a flicker of danger as Roberto Firmino's dangerous cross was scrambled away.
Moments later, PSG threatened again as Neymar found Mbappe down the left and his low cross just eluded Edinson Cavani.
Gomez was booked for a foul on Neymar after 33 minutes, but things got far worse for the visitors three minutes later as PSG put themselves firmly in control.
The goal came from another rapid break down the left and, when Mbappe produced another low cross, Alisson denied Cavani from close range only for Neymar to sweep the rebound into the corner.
But Liverpool grabbed a lifeline right on half-time when Sadio Mane raced into the area and Di Maria sent him tumbling, Milner blasting the penalty past Gianluigi Buffon.
Three minutes after the break, PSG thought they had added a third but Marquinhos was offside when he prodded home a dangerous Di Maria free-kick.
But the home side were failing to find the intensity with which they had started the game, Milner and Firmino linking before Thiago Silva cleared and then Andrew Robertson's cross headed wide by Firmino.
PSG coach Thomas Tuchel had seen enough and made a double change, Eric Maxim Choupo-Moting and Dani Alves replacing Cavani and Di Maria, Liverpool bringing on Naby Keita for Wijnaldum soon afterwards.
Marquinhos had a header saved by Alisson after Neymar's cross as the home side tried to step up the pace, but there was an increasing sense of nervousness in the home crowd as the game approached its final 20 minutes.
Liverpool, who had brought on Daniel Sturridge for Firmino, then brought on Xherdan Shaqiri for Milner, but with 10 minutes to go they were under pressure as Neymar raced into the area and went down under Van Dijk's challenge with the referee waving play on.
Mbappe shot over before being replaced by Adrien Rabiot as PSG held on for a crucial three points to leave Liverpool needing to beat Napoli on the final day of the group or hope PSG are beaten at Red Star Belgrade.
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