Both teams showed intent as they looked to gain an early advantage with so much at stake, although neither goalkeeper was initially tested, as Chris Richards blocked Roberto Piccoli’s attempt and Jean-Philippe Mateta guided a header wide.
Robin Gosens then had a major opening when Giovanni Fabbian trickled through the box before finding the German, who couldn’t control the ball enough to get it on target.
By contrast, Evann Guessand had much less time to think when Daniel Munoz fizzed the ball to the forward in the box, and his instinctive attempt trickled past the post.
Guessand failed to hit the target with another shot shortly after, but he drew a challenge from Dodo that resulted in a penalty and a yellow card that will keep La Viola’s right-back out of the second leg.
Though goalless since January 25th, Mateta fearlessly stepped up, sending David de Gea the wrong way with 24 minutes on the clock.
Mateta was denied by a superb De Gea save just seven minutes later, although Tyrick Mitchell was in position to send his follow-up past Marin Pongracic and in off the post.
And just before half-time, Jaydee Canvot saw a shot saved before Maxence Lacroix sent his attempt wide.
The hosts had shown no sign of letting up as the break approached, but they were dealt a scare shortly after the restart, with Fabbian smashing the ball against Dean Henderson from a Dodo cutback.
Daichi Kamada responded by hitting the side netting, yet there were more positive signs for the visitors, with Albert Gudmundsson and Piccoli bringing saves out of Henderson moments apart just before the hour mark.
Guessand was forced off injured in a blow for the hosts, yet they prevented any damage being done to the scoreline and threatened going the other way, with Ismaila Sarr and Mateta sending a header apiece wide.
But Sarr made no mistake from Kamada’s 91st-minute cross, heading the ball into the floor and into the top corner to make Palace's aggregate cushion look far more robust.
That could prove to be a vital moment in the tie, and it put the proverbial icing on Palace’s fifth consecutive match unbeaten - also their first 90-minute win in four attempts - and put the Eagles in a commanding position ahead of the second leg at the Stadio Artemio Franchi.
Meanwhile, it’s a first defeat in seven across all competitions for Fiorentina, who now face an uphill battle to avoid yet more UECL heartbreak.