Kylian Mbappe seemed to have salvaged a point for his side, before Firmino's superb low drive in to the bottom corner with seconds to spare.
James Milner doubled the advantage via a penalty before Thomas Meunier pulled one back for the visitors.
Team-mate Andrew Robertson, who set up Sturridge for his goal against PSG, says the England striker is "ready to go" if called upon by Klopp, after praising his performance against the French champions.
The Brazil global made the difference with a brilliant 91st-minute victor, celebrating by covering up his eye, but Klopp made sure he highlighted Sturridge's contribution. Liverpool did have another shout for a goal when Mohamed Salah got a tap in on the goal line which was called back due to a foul on Sturridge to Alphonse Areola's groin.
He was benched for the start of Liverpool's showdown with PSG, but came on to score a crucial goal and will start this weekend.
Thomas Meunier's low volley cut Liverpool's lead in the first half and the Belgium worldwide suggested PSG should consider following the Reds' tactical plan.
"I was thinking about that today".
Over the years we have become accustomed to Brazilian superstar Neymar making defenders look silly as he leaves them for dead with outrageous skills moves. "Obviously we lost a goal just before half-time and so 2-1's a wee bit uncomfortable", he said.
"We covered a lot of yards and closed all the gaps and when we had the ball made them run and used the right wing".
"It's a tough atmosphere to play in once they're behind us". We know the players they've got but it's probably the only time they really opened us up.
PSG's talisman Neymar showed a real touch of class during the journey back to the team coach by interrupting one of Firmino's interviews to congratulate him on his impactful cameo appearances, and a video of the incident has even been shared on social media.