After a goalless first-half at Selhurst Park, the Magpies fell behind shortly after the restart following Mateta's composed finish, completing a dangerous move with Jordan Ayew before slotting home.
The French striker then confirmed maximum points for the Eagles in the closing stages after his drilled close-range effort from Will Hughes' cutback rounded off a difficult evening in the capital for Eddie Howe's side, who recorded a mere two shots on target during the contest.
The Magpies head coach named an unchanged starting XI from the side which claimed an impressive 4-0 win against Tottenham Hotspur, 11 days ago with Callum Wilson named on the substitutes' bench after suffering a pectoral injury in February.
The hosts created the opening goalscoring opportunity of the contest through Ebere Eze as the Palace forward picked the ball up in a dangerous position and, after twisting and turning, fired a low strike narrowly wide of the right-hand post.
The Magpies withstood a further attempt on goal minutes later as Mateta rose high from Eze's curling cross from the right flank but the Frenchman's header was directed over the crossbar.
Magpies goalkeeper Martin Dúbravka, targeting a third successive clean sheet, was forced into action shortly after as the Slovakian shot-stopper held Adam Wharton's vicious drive from distance.
Alexander Isak went close to netting his 18th Premier League goal of the 2023/24 campaign as the Swedish forward raced onto Bruno Guimarães' lofted through ball and evaded the challenge of Joachim Andersen but his heavy touch beyond the Danish defender allowed Palace goalkeeper Dean Henderson to race out of goal before producing an unorthodox slide tackle to deny the in-form frontman.
In the 55th minute, Newcastle were delivered a tough blow as Mateta broke the deadlock for the hosts. After Eze's pass was fizzed into the striker's path, the Frenchman completed a quick one-two with Jordan Ayew before slotting the ball into the bottom left-hand corner.
Dúbravka denied Mateta from doubling his and Palace's tally shortly after as the goalkeeper importantly held the physical forward's header following Eze's teasing corner from the right flank.
Will Hughes almost punished United after the hour mark as the central midfielder's first-time curling effort from the edge of the box flew inches over the crossbar.
Newcastle were appealing a penalty in the closing stages as Sean Longstaff went down inside the box after Hughes looked to have tugged the midfielder's arm but referee Thomas Bramall waved away the decision, despite a VAR intervention, to the frustration of the United players.
Elliot Anderson was unable to net a late equaliser on his 50th appearance for his boyhood club as the 21-year-old midfielder, still awaiting his first competitive goal for the Magpies, saw a tame header from Dan Burn's cross comfortably saved by Henderson.
In the 88th minute, Mateta netted his and Palace's second goal of the evening. After Jeffrey Schlupp and Will Hughes combined down the left flank, the latter cut the ball into Mateta's path, who drilled a low effort through the legs of Dúbravka.
Anthony Gordon went close to halving the deficit in stoppage-time after racing onto Isak's pass and, after chopping inside, saw a fierce shot at goal blocked by Henderson as the Magpies dropped into seventh place, three points adrift of sixth-placed Manchester United.
