Kylian Mbappe appeared to have salvaged a draw for PSG after levelling the scores in the 83rd minute, but the World Cup winner then gave away possession 25 yards out from his own goal.
And Firmino, who started on the bench due to an eye injury suffered against Tottenham on Saturday, rifled across Alphonse Areola to ensure last season's beaten finalists got off to a victorious start in Group C on Tuesday.
PSG had fought back from 2-0 down, Liverpool leading thanks to a Daniel Sturridge header and James Milner's penalty, but Jurgen Klopp's men deserved to come out on top.
Virgil van Dijk and Milner forced early saves from Alphonse Areola, with the visitors having to defend a barrage of corners, and Liverpool took the lead on the half-hour mark.
Trent Alexander-Arnold's delivery from the right was slightly too deep but Andrew Robertson arrived to deliver a brilliant first-time cross that Sturridge firmly headed past Areola.
The Liverpool lead was soon doubled, Milner beating Areola from 12 yards after Juan Bernat clumsily tripped Georginio Wijnaldum in the penalty area, but Thomas Meunier gave PSG an immediate lifeline with a low volley.
Liverpool thought they had restored their two-goal cushion after the break when Mohamed Salah tapped in from close range, but it was rightly ruled out for Sturridge's challenge on Areola.
Mbappe, who had barely had a sniff of goal, seized on a loose ball after Neymar's driving run to slam home past Alisson and seemingly earn PSG a point with only seven minutes to go.
However, the France international crucially had an impact at the opposite end of the field in added time, giving up possession to allow Van Dijk to feed Firmino, who arrowed in a shot to settle a pulsating contest.
What does it mean: Liverpool in ominous form
With six wins out of six this season, Liverpool are sending a message to the Premier League - and now the rest of Europe. Having reached the final last season, where they were undone by Salah's injury and Loris Karius' errors, they look in good shape for another extended run in 2018-19, although they left it extremely late after showing familiar defensive frailties.
Pat on the back: Firmino makes the difference
Only fit for the bench due to the painful eye injury sustained at Wembley, Firmino had not even trained the day before the match. But he showed there was nothing wrong with his radar to make sure the Reds collected the three points their performance undoubtedly deserved. Sturridge may have scored in deputising for the Brazilian, but Firmino demonstrated his huge importance to this Liverpool side.
Boot up the backside: Salah lacks influence
Salah was perhaps slightly unfortunate to have his goal ruled out, but the Egypt forward lacked his usual snap and sparkle and seemed a touch off the pace. And he was fortunate Firmino bailed him out after he had cheaply coughed up possession prior to Mbappe's leveller.
Key Opta stats:
- Liverpool have won their opening six competitive matches of a season for the first time since 1961-62.
- PSG are winless in their last five Champions League matches against English sides (D3 L2) and have only kept one clean sheet in their previous 13 such games, a 0-0 draw at Stamford Bridge during the 2004/05 group stages.
- Since he joined Liverpool in the summer of 2015, only Sergio Aguero (17) and Harry Kane (15) have scored more penalties in all competitions for a Premier League club than Milner (13).
- Sturridge has been directly involved in a goal in each of his last four Champions League appearances for Liverpool (2 goals, 2 assists).
- Since the start of last season, Liverpool have scored 44 Champions League goals; 11 more than any other team in the competition in this period.
Liverpool and PSG put their perfect domestic records on the line against Southampton and Rennes respectively at the weekend. When the Champions League returns, PSG host Red Star Belgrade with Liverpool travelling to Napoli.