Goals from Mateta, making his first start since January, Tyrick Mitchell and Ismaïla Sarr topped off a near perfect evening for the Eagles.
If anything Palace could have had more, with substitute Yéremy Pino going close twice after coming on, as Oliver Glasner's team dominated their Serie A opponents.
Mateta set the team on their way by converting a 24th minute penalty and later completed a lap of honour applauding Selhurst Park after the game.
He told Palace TV: "I'm very happy and I'm very happy for the team as well. We did the job at home and now it's time to do the job away too.
"It was a fantastic performance from the team, from the lads, even from the people who came on.
"It was a fantastic night and we're focused on Newcastle for the next game."