Carlo Ancelotti was dealt a blow before kick-off when goalkeeper Thibaut Courtois had to be withdrawn from the starting line-up due to injury, to be replaced by Andriy Lunin.
His mood would not have improved after kick-off as the hosts stormed into an early lead when Dani Rodriguez’s cross looped off the head of Real Madrid defender Nacho and into the top corner.
Real struggled to break down a stubborn defensive resolve put up by Javier Aguirre’s side, leading to reckless long-range shots from Rodrygo, Antonio Rüdiger and Ernesto Valverde floating harmlessly wide.
But the visitors were given a route back into the game when they were awarded a penalty early in the second half after Predrag Rajkovic had brought down VinÃcius JunÃor.
However, the Serbian shot-stopper redeemed himself by guessing the right away to keep out Asensio’s spot-kick.
Ancelotti turned to the likes of Luka Modric, Toni Kroos and David Alaba from the bench but Mallorca held firm leaving Real five points behind the league leaders Barcelona, who can extend that gap when they face Sevilla later on Sunday.
The European champions head off to the Club World Cup on the back of a defeat.
Atletico Madrid were unable to tighten their grip on fourth place in La Liga as they fell to a 1-1 draw with lowly Getafe on Saturday.
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.
Diego 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.
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 Dejene Dakonam 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.