The Eagles will look to finish the job in Italy next week with the second leg taking place on Thursday evening (20:00 BST).
But how is the rest of the line-up for the last four looking at half-time in the quarter-finals?
Here’s everything else that went down on the first night of action, on a night where the home sides dominated...
#### **Shakhtar treble sees off AZ**
The prospect of Palace reuniting with league phase opponents AZ Alkmaar in the semi-finals now seems remote after the first legs.
AZ, who currently lie sixth in the Dutch league, were comfortably beaten by Shakhtar Donetsk in Krakow, thanks to three goals in 11 second-half minutes.
Attacking midfielder Pedrinho went close in the second half when his curling free-kick crashed off the woodwork but he pounced on a loose ball to fire an unstoppable effort in off the bar for the opener.
With AZ then trying to push numbers forward to get back level, they were hit with two quickfire sucker punches.
Alisson Santana netted twice in three minutes to have the Ukrainian side a 3-0 lead going into the return match in the Netherlands next week. Should Palace progress to the semi-finals, they will face the winner of this tie with the second leg taking place at Selhurst Park.
Rayo Vallecano seized the initiative of their tie with AEK Athens in the early kick-off, with a dominant performance.
They got off to a dream start when lias Akhomach struck inside two minutes in front of a partisan home crowd.
It was 2-0 in first-half stoppage time when former Bilbao midfielder Unai Lopez reacted quickly after Thomas Strakosha saved Akhomach’s effort.
AEK Athens improved after the break but were unable to get themselves on the scoresheet.
And when a VAR review deemed there was a handball in the AEK penalty area, Isi Palazón converted to seal a 3-0 win for the La Liga side, leaving the Greeks with an uphill task in the second leg.
One of the pre-season tournament favourites Strasbourg will now require a huge turnaround to reach the last four.
The French side suffered a bad night in Germany, going down 2-0 to Mainz 05. The Bundesliga outfit scored two stunning goals, the first coming from Kaishu Sano's curled 11th-minute effort, in off the post.
Austrian defender Stefan Posch then made it two inside the first twenty minutes for the hosts when side-footing home a volley from a corner.
Strasbourg did have chances to get back in the first leg, but can also had to count on goalkeeper Mike Penders to ensure are still in the tie. The Belgian stopper made a number of key saves, while Valentin Barco hit the crossbar at the other end.
It was the first time all season that Strasbourg have tasted defeat in the Conference League, ending their unbeaten European run at the 11th game.
#### **UEFA Conference League quarter-final first leg results;**
* **Palace 3-0 Fiorentina**
* Shakhtar 3-0 AZ Alkmaar
* Rayo Vallecano 3-0 AEK Athens
* Mainz 2-0 Strasbourg