Atletico draw with Getafe, Elche finally win
Angel Correa sent Atletico ahead in the derby clash but Enes Unal clinically converted a penalty to level for the relegation-battling visitors.
Saul, who was Atletico's hero last weekend off the bench, scoring the winner against Osasuna, became the villain at the Metropolitano.
The Spanish midfielder handled Borja Mayoral's header in the box to concede the penalty a few minutes after coming on.
"We went in front making a great effort, we tried in every way, we played the game we wanted to play," Atletico coach Diego Simeone told DAZN.
"Circumstances are not predictable, we didn't get the second goal and what appears in football appeared -- a penalty in a play which was not dangerous.
"But we have to keep improving."
Simeone's side dominated the first half but failed to create many clear chances.
However they moved ahead on the hour mark when Correa fired home after Thomas Lemar's shot was saved.
The goal was initially flagged offside but was awarded after checking on VAR, by which time Correa had been substituted, celebrating his strike already wearing a big coat on the sidelines.
"The play for the goal was a bit weird," Correa told DAZN.
"They thought it was offside, there were doubts about it, then Cholo made the change and in the end it was a goal, it was a bit strange."
Correa also said he thought his team deserved a penalty when Getafe's Djene Dakonam appeared to drag down Alvaro Morata in the area in the first half.
"I think it was a clear penalty on Alvaro and a second yellow card for the defender," added Correa.
"But it's always the same for us. We don't want them to gift us anything, just be fair, because it was a clear penalty."
Atletico's joy was shortlived, with Unal firing home from the spot in the 83rd minute after Saul's handball.
Yannick Carrasco flashed a shot wide after a surging run down the left flank as Atletico chased a late winner.
The Belgium winger wildly hammered another effort over the bar from distance with Simeone urging his team forward from the sidelines.
Atletico striker Memphis Depay, on as a substitute, angrily appealed for a penalty when he tangled with Djene in the box but referee Mateu Lahoz ignored him.
Getafe goalkeeper David Soria made a fine save to keep the Dutch forward at bay at the death.
Atletico stay fourth but missed a chance to move closer to Real Sociedad, third, four points above the Rojiblancos with a game in hand.
Getafe are 19th on 18 points, two from safety.20th time lucky
Earlier, La Liga's bottom side Elche stunned Villarreal 3-1, winning their first game all season.
The Yellow Submarine, provisionally fifth, are chasing Champions League qualification but were sunk by a Pere Milla hat-trick at the Manuel Martinez Valero Stadium.
Elche did not manage a win in the first half of the season but finally triumphed in their 20th game, with Milla firing home in the third minute to open the scoring.
Gerard Moreno levelled but Elche moved ahead in stoppage time at the end of the first half.
Milla converted a penalty after Jorge Cuenca brought down Ezequiel Ponce to restore the advantage for Pablo Machin's side.
The forward then netted again from the spot after he had been fouled in the second half to seal his team's win, although he was taken off injured before the hour mark.
Elche, on nine points, are 11 from safety and have played a game more than Valladolid, 17th, who face Real Sociedad on Sunday.
Espanyol shared a 1-1 draw with Osasuna, Martin Braithwaite equalising for the hosts after Ante Budimir's opener.
Both sides finished with 10 men after Ez Abde and Ronael Pierre-Gabriel were dismissed for second yellow cards in the first half as they scrapped with each other.