Their hopes of progressing to the next stage of the league are hanging in the balance.
In the first half, Luka Jovic, Nicolas Gonzalez, and Antonin Barak all scored for the visitors.
Gonzalez restored the four- goal cushion from the penalty spot after Stephen Humphrys pulled one back for the visitors.
It means that Hearts have to win their two remaining group games against RFS and Istanbul Basaksehir and hope that they only get one point from their remaining games.
The two of them talked before the game about being positive.
"We felt like we weren't getting up the park enough and this game we were up and at it, but against a physical team you have to double your effort and it wasn't until the second half that we did that."
After a loss to Lazio on Monday, Fiorentina came into this game looking to get back on track.
Barrie McKay was on the receiving end of an uncharacteristically loose pass. Humphrys tried to shoot across Pierluigi Gollini but his low strike came back off the post.
After forcing a good save out of Gordon, and then taking the lead, it seemed to shake Fiorentina into life.
A short corner caught Hearts cold, and a pin-point cross from home captainBiraghi picked out Jovic just outside the six-yard box. The former Real Madrid man headed down into the corner without a second thought.
The hosts did not have to wait long before doubling their lead after Mandragora struck a fierce shot that crashed away off the post.
After a soft free-kick went to the edge of the Hearts area, Biraghi struck a beautifully judged shot up and over the wall into the top corner. The award was harsh, but Fiorentina were deserving of their two goals.
The half-hour mark was when things got worse for Hearts. Gonzalez was able to roll a shot back across Gordon and into the far corner after some intricate passing on the edge of the visitors' box.
The away goal was breached again on 38 minutes when the fourth goal was scored. The Ivorian pulled the ball back to his teammate, who made no mistake from 12 yards.
Humphrys was put in on goal just as he was in the first half, and he rolled a low shot past Gollini.
They put up a fight in the second half, but it was too little, too late as the game was already out of reach. The referee pointed to the spot when the hosts broke into the Hearts box, after Alex Cochrane kicked out at the Hearts player.
Gonzalez sent Gordon the wrong way to score his second goal of the night.
After being introduced off the bench, Shankland saw a speculative effort drift onto the roof of the net after he spotted Gollini off his line, but the home team easily saw out the last 10 minutes.
There are injuries at the back, but they are shipping goals at an alarming rate. Fourteen goals have been scored against them in their last four games.
The ease with which they sliced through Hearts will be worrying. Last week it was a simple ball into the box that broke the deadlock at Tynecastle, and again in Tuscany.
With a run of tricky games leading up to the World Cup, the Hearts boss needs to find a way to shore up his defence.
On Sunday, Hearts will play a game with Aberdeen.
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