The visitors grabbed a late winner through Alberto Gilardino in the second minute of added time to clinch top spot.
Looking at the positives, Liverpool started with Alberto Aquilani at last – and Fernando Torres returned from a groin injury for the final 25 minutes.
Yossi Benayoun’s first-half header gave Liverpool hope in a game they largely controlled, but defensive uncertainty gave Martin Jorgensen the chance to drive home the equaliser in the second period.
Fiorentina, aware that Lyon were hammering Debrecen, realised they needed to win to make sure of top spot in the group, and they piled on some belated pressure.
It paid off and Liverpool were to suffer yet another late goal disaster.