The Eagles were the better side from start to finish on home soil, and a double from Mateta allowed the capital outfit to post a third straight win in England's top flight.
Oliver Glasner's side remain 14th in the table, but they are now 14 points clear of the relegation zone and therefore their spot in England's top flight for next season has been guaranteed.
Newcastle, meanwhile, have dropped to seventh spot, with Manchester United moving into sixth courtesy of their 4-2 home success over Sheffield United.
Palace make it three league wins in a row
Palace had a golden chance to take the lead in the early exchanges when the ball fell kindly for Joachim Andersen inside the Newcastle box, but Fabian Schar was on hand to make a brilliant block.
The Eagles had another opportunity in the 15th minute, with Mateta meeting a cross from Eberechi Eze, but his looping header was over the crossbar.
Jordan Ayew then hit the side-netting in the 28th minute, and it was all Palace at Selhurst Park, with Newcastle struggling to carve out any opportunities of note.
Alexander Isak did manage to break into a one-on-one situation with Palace goalkeeper Dean Henderson late in the half, but the Englishman came out bravely to deny the centre-forward.
Jean-Philippe Mateta continues his excellent form
Palace had nine attempts in the opening 45 minutes to Newcastle's one, which told the story of the first period, with the hosts also registering three shots on target, but they had nothing to show for their dominance.
The Eagles have actually stopped the opposition from scoring a first-half goal in 21 of their 34 league matches this term, and they managed to make the breakthrough early in the second period in this contest.
Mateta had caused Newcastle all sorts of issues in the opening 45 minutes, so it came as no surprise when he was the player to make the breakthrough in the 55th minute, with the forward combining brilliantly with Ayew before picking out the back of the net in emphatic fashion.
Newcastle had a shout for a penalty in the 77th minute when Sean Longstaff tumbled inside the box under a challenge from Will Hughes, but the referee said no and VAR agreed, much to the away side's frustration.
Palace then doubled their lead in the 88th minute, with Mateta driving a low cross from Hughes through the legs of Newcastle goalkeeper Martin Dubravka.
Mateta has now netted 11 Premier League goals this season, including eight under the management of Glasner, with the 26-year-old finishing the campaign in excellent form.