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.
