Mateta scored the only goal of a scrappy game on the half-hour mark to ease the pressure on manager Oliver Glasner and lift them out of the relegation zone.
The Eagles thoroughly deserved their victory, working tirelessly to close down Tottenham, who looked strangely muted and never showed the sort of form that had taken them to seven wins in their previous eight game. Ange Postecoglou cut a forlorn figure on the sidelines as he saw another disappointing display from his side, who have slipped down to eighth place.
Tottenham struggled to get their passing game going for the opening hour, in part because of their own sloppiness but mainly because Palace closed down the supply lines so well, pressing all over the pitch and not allowing Spurs to play out from the back as they like to do.
The press was led from the front by Mateta, back in the side and back among the goals after half an hour. The move began when Tottenham were unable to play out from defence, with Micky Van de Ven losing possession to Daniel Munoz, whose cross arrived at the feet of Mateta via Eberechi Eze. The big striker, unmarked on the left of the penalty area, had time to measure his shot and drove the ball low and powerfully through the legs of Pedro Porro and Guglielmo Vicario.
Palce deserved their lead, having shown more energy and determination to win 50-50 challenges in what was a scrappy and bad-tempered first-half. Three players required treatment for head injuries, and Jefferson Lerma limped off with what looked like a hamstring problem.
His replacement Will Hughes brought even more energy, however, and also chipped in a clever cross that Maxence Lacrois managed to head over from close range. His fellow centre-back Marc Guehi also had a good chance later in the half, but headed tamely at Vicario.
Dean Henderson, in the opposite goal, was not unduly troubled until the closing stages of the half, when he tipped away a James Maddison shot. Dejan Kulusesvski had a shot deflected on to the post before the break and was denied by Henderson saving at his feet shortly after the restart.
But Vicario was busy too, using his feet to save Ismaila Sarr's deflected shot and than grateful to see an offside flag rule out an effort from Eze that crept past him.
Ange Postecoglou had given a full league debut to Mikey Moore, the teenage tyro who had impressed on his full European debut against AZ Alkmaar. Timo Werner made way, but later replaced Moore, who struggled to get into the game.
Postecoglou also hooked Maddison and Kulusevski, sending on Pape Matar Sarr and Richarlison as well. But the Brazilian looked rusty after a long injury lay-off and spurned two half-chances as Tottenham chased an equaliser.
Palace almost increased their lead ten minutes from the end whenAdam Wharton hit a piledriver from 25 yards that forced Vicario to save at full stretch.
It mattered little when referee Darren Bond, who was roundly booed by both sets of supporters for some strange decisions, blew the final whistle, allowing Palace celebrations to begin.
C Palace (5-4-1): Henderson 7; Munoz 7, Lacroix 8, Chalobah 8, Guehi 8, Mitchell 7; Sarr 7 (Nketiah 67), Wharton 7 (Kamada 87), Lerma 6 (Hughes 22), Eze 7; Mateta 7.
Tottenham (4-3-3): Vicario 7; Porro 6, Romero 6, van de Ven 6, Udogie 6; Kulusevski 6 (Richarlison 62), Bissouma 6 (Bentancur 87), Maddison 6 (Sarr 62); Johnson 6, Solanke 7, Moore 6 (Werner 62).
Referee: Darren Bond 5/10