Real Madrid lost ground on La Liga leaders Atletico Madrid after a disappointing draw at Elche.
Fidel struck a second-half penalty to earn his side a point and end Real’s run of five consecutive league wins.
Luka Modric had opened the scoring from close range after Marco Asensio’s long-range effort came back off the crossbar.
Second-placed Real are two points behind neighbours Atletico, who also have two games in hand.
Atletico had ensured they would end 2020 top of the table with victory over Getafe earlier on Wednesday, and Real never got going in response.
Modric handed the visitors the lead when he reacted first to the loose ball after Asensio’s fierce effort, but they were pegged back five minutes after the interval.
Dani Carvajal hauled down Antonio Barragan inside the area, and Fidel levelled the scores with an emphatic spot-kick to the bottom left corner.
Carvajal nearly made amends 20 minutes later when he controlled an excellent pass from Toni Kroos and fired at goal, but Edgar Badía produced a smart save to deny the Real defender.