Ralph Hasenhuttl’s side took to the French Riviera desperate to claw their way back into the reckoning in Group G, having fallen behind in the early stages.
With both Besiktas and FC Porto peeling away into the qualification spots for the last 16, Leipzig needed a victory over Monaco to ensure they remained in the race.
And they produced the perfect display as Keita added to his increasing list of milestones with his first-ever Champions League goal.
The night got off to the ideal start as struggling Monaco centre-back Jemerson turned Marcel Sabitzer’s cross into his own net within six minutes.
Leipzig made it a quick-fire double as Liverpool target Timo Werner and Slovenia midfielder Kevin Kampl, who Jurgen Klopp signed while at Borussia Dortmund, combined for a fine second.
Falcao reduced the deficit just before half-time, beating former Reds goalkeeper Peter Gulacsi in the air to head home Marcos Lopes’ free-kick from deep.
But Keita restored Leipzig’s lead in stoppage time of the first half, with a beautifully worked goal.
Picking up Marcel Halstenberg’s heavy pass with his back to goal outside the penalty area, Keita swiftly turned free of Kamil Glik and Fabinho and sidefooted past Danijel Subasic to make it 4-1.
Leipzig now need to a result against Besiktas, and Porto’s home clash with Monaco to go in their favour, on December 6 in order to progress to the knockout stage.
Their victory over Leonardo Jardim’s side has already secured a place in the Europa League‘s last 16, but for the likes of Keita, Werner and Emil Forsberg, this should not be enough.
Keita is Liverpool’s club-record signing, with the Reds having paid £55 million for his services last summer.
While they are reported to have harboured hopes of convincing Leipzig to part ways with the 22-year-old before next summer’s agreed date, this is unlikely.
The Guinea international has now scored three goals and laid on one assist in 15 games in all competitions, which is a significant drop-off from his eight goals and eight assists last term.
But Klopp will not be concerned, as Keita has proved himself a talent with top-level potential.