The Brazil forward was a late substitute having damaged an eye at Spurs on Saturday and struck a superb finish after Kylian Mbappé had equalised for Thomas Tuchel's team in the 83rd minute.
Meunier grabbed a goal back for his side before half-time, taking advantage of some lacklustre Liverpool defending.
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.
"It was really important we started like we did".
"We played with a lot of bravery and mental strength". I have never seen him as fit as he is in the moment.
Their Champions League cameos came a year to the day that the Potters were beaten 2-0 by Bristol City in the Carabao Cup.
But, Roberto Firmino of Brazil came off the bench and scored the victor for Liverpool, moments before the final whistle.
The Englishman looked a new man in Liverpool colours, seemingly rediscovering his confidence and belief after a positive preseason that followed a rather tumultuous 2017-18, during which he failed to make an impact at Liverpool and had a disappointing loan spell at West Bromwich Albion.
He responded by opening the scoring on the half-hour with a fine header and throughout the game Sturridge was a strong physical threat and effective link-up player. Firmino celebrated by running towards the crowd with one hand covered over his wounded eye, much to Klopp's amusement.
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. "I loved his goal celebration".