Fiorentina picked up their first points of the season in Europe thanks to a brace in the space of ten minutes from young striker Stevan Jovetic, who was making his first start in the Champions League.
The 19-year-old produced two smart finishes to stun Rafael Benitez, who had claimed on the same day that his side were capable of beating anybody.
Despite a bright opening from Liverpool, it was Fiorentina who were much in the ascendancy for virtually the entire first half at Artemio Franchi.
La Viola enjoyed long periods of possession after a nervy start in the first period and converted their dominance into a lead on 28 minutes as Jovetic took full advantage of a Liverpool back four who were waiting for an offside flag that never came.
Cristiano Zanetti skipped away from the pedestrian Lucas Leiva and Fabio Aurelio, who struggled in an unfamiliar central midfield role, before sliding a pass through to Jovetic who made his way into the area as the Reds back four froze in confusion with Adrian Mutu in an offside position.
Jovetic played to the whistle and calmly slotted past Pepe Reina to make it 1-0, before an onslaught came from the Serie A outfit.
He made it two when a fierce Juan Manuel Vargas shot was toe-poked on by Jovetic to beat Reina at his near post.
Liverpool came out for the second half a different side and tried everything to get back into the game. A glaring Lucas miss from a corner highlighted the Reds' frustrations, while captain Steven Gerrard also failed with a looping header.
Fernando Torres had a penalty claim waved away, before volleying over from close range after good work by Martin Skrtel.
The match signalled the first time Liverpool had failed to score in 22 European outings, and it was also the Reds' third loss of the season.