Jurgen Klopp rotated his side amid a hectic fixture list but was made to pay as quick fire second-half goals from Josep Ilicic and Robin Gosens secured victory for the Italian side.
After the home side fielded an experimental lineup featuring three teenagers in Rhys Williams, Neco Williams and Curtis Jones, Ilicic put the visitors ahead on the hour mark with a deft volley from an inswinging cross from Alejandro Gomez.
Liverpool boss Juergen Klopp reshuffled his pack, bringing Roberto Firmino, Fabinho, Diogo Jota and Andy Robertson off the bench, but his side quickly conceded a second as Gosens volleyed home Hans Hateboer's knockdown from close range in the 63rd minute.
Liverpool could not bounce back and though they still lead the group on nine points, both Atalanta and Ajax Amsterdam, who beat bottom side Midtjylland 3-1, are now two points behind with two games left to play.
Securing their knockout spot with two games to spare would also have given Klopp precious opportunity to rest his star names in the remaining fixtures.
Additional reporting by Reuters.