Mateta, making his first Palace start since a proposed move to AC Milan collapsed in January, converted from the penalty spot after 24 minutes after Evann Guessand was fouled by Fiorentina defender Dodo.
The French striker also had a role in Palace’s second goal seven minutes later as Tyrick Mitchell finished off after Mateta’s close-range effort had been blocked by Fiorentina goalkeeper David de Gea.
“I keep working hard, and I’m always here to push for the victory,” Mateta told TNT Sports. “Today we did it, but it’s not finished. We have one more game in Italy.”
Fiorentina pushed back after the break with Giovanni Fabbian rattling the woodwork after 51 minutes and goalkeeper Dean Henderson pulling off two saves for the hosts just before the hour.
But Ismaila Sarr ensured Palace take a comfortable advance to Tuscany next week when he headed in on the 90th minute.
A semi-final tie against either Shakhtar Donetsk or Dutch side AZ Alkmaar awaits either Palace or Fiorentina.
Ukrainian side Shakhtar beat AZ 3-0 with all goals late. Pedrinho got the first after 72 minutes followed by a quickfire Alisson Santana brace with 10 minutes to go.
Spanish club Rayo Vallecano are one step away from playing in a European semi-final for the first in their history following a 3-0 win against AEK Athens.
The winner will play either Mainz or Strasbourg.
Moroccan winger Ilias Akhomach opened the scoring after two minutes in the suburbs of Madrid finishing off an Alvaro García cross.
Unai Lopez added a second off a rebound just before the break with Rayo captain Isi Palazon scoring the third from the penalty spot after 74 minutes.
German club Mainz beat French outfit Strasbourg 2-0 to maintain their unbeaten record at home this season in the competition with six wins out of six. (AFP)
