This was their first away defeat in Europe since the semi-final defeat at Chelsea in April 2008, and only their ninth away reverse in 38 attempts in the competition under boss Rafael Benitez.
Montenegro international Stevan Jovetic did the damage with a quick-fire double inside 10 first-half minutes.
Liverpool had no answer to the 19-year-old's drive and pace, and their Group E future is now under serious threat.
Liverpool did not manage a shot on target in a disappointing first period and although they fought back after the break, Fiorentina were not going to let a prized victory escape their grasp.
Benitez's response to the loss of Javier Mascherano with a hamstring injury was to recall Brazilian defender Fabio Aurelio to his side.
Aurelio has had only a Carling Cup run-out against Leeds after a summer knee operation, and he was be used in a midfield role against the Italians, who are fourth in Serie A.
Otherwise it was the same Liverpool side that beat Debrecen in the first group match.
Aurelio was used in a holding midfield role to allow Steven Gerrard to continue his advanced role supporting Fernando Torres.
But it barely worked, with Fiorentina quicker and more mobile. Martin Skrtel, at the back, had to be at his best to halt a run and shot from Jovetic, who from the resulting corner set up Marco Marchionni for an overhead effort that just cleared the bar.
Jovetic saw another effort flash wide after 22 minutes, Adrian Mutu having created the opening having beaten both Lucas and Aurelio in midfield.
There had been constant indecision in the Liverpool defence, and a failure to retain possession in midfield, and they were punished after 27 minutes.