A first-half goal by Luka Modric was cancelled out by a Fidel Chaves penalty in the second half to ensure that Real Madrid and Elche shared the spoils at the Estadio Martinez Valero on Wednesday night.
In what was an emphatic start to the game, Real Madrid came roaring out of the blocks and fashioned their first chance as early as the third minute.
Spain international Lucas Vazquez put in a great cross into the box but an unmarked Toni Kroos somehow managed to head wide from six yards.
Their sustained pressure continued, and Marcelo hit the bar with a right-footed shot after some good interplay with Casemiro.
Real Madrid soon got the lead their start deserved when their high press saw them win the ball up the field with space left behind.
Marco Asensio charged forward and hit a perfectly struck shot that rattled the bar, giving us the rare sight of Luka Modric heading the ball into an unguarded net on the rebound.
This was the first headed goal by the Croatia international since he scored for Tottenham Hotspur against Wigan in the FA Cup in 2009.
This goal was the difference between the sides in the first half, and Real Madrid went into the break in the ascendancy.
The hosts, however, came out for the second half in high spirits and were awarded a penalty when Dani Carvajal was adjudged to have pulled down Antonio Barragan in the area.
The incident left referee Jorge Vazquez with no choice but to point to the spot. Chaves buried the ensuing penalty beneath the dive of Thibaut Courtois.
Emiliano Rigoni was the brightest spark in the Elche team. The Argentine created a chance for Lucas Boye who struck the post after some good footwork in the box on the hour mark.
Real Madrid cranked up the pressure in the dying stages of the game, with Toni Kross finding Carvajal with an excellent cross-field ball from 35 yards. The defender showed great technique to control and strike a left-footed shot that was well-saved by Edgar Badia.
The Elche goalkeeper was called into action almost immediately when he saved a shot from Sergio Ramos at point-blank range to the disbelief of the Real Madrid captain.
Despite holding most of the possession in the dying stages of the game, the capital side failed to create clear-cut chances. The draw was hardly the result that Real Madrid would have envisaged.
Here, we shall have a rundown of five talking points from the fixture.
#5 Atletico Madrid have the advantage in the title race
With Barcelona flattering to deceive in Catalunya, the onus has fallen on the Madrid sides to set the pace in the title race.
Real Madrid's victory in El Derbi Madrileño earlier in the month had put them right back into the title race. However, this latest setback has handed the initiative back to their city rivals.
Atletico Madrid had earlier secured a hard-fought 1-0 victory over Getafe to go three points clear at the summit. Zidane's side knew that anything other than a win was simply not good enough.
As it happened, the defending champions failed to get the job done in Valencia. This stalemate means that Atletico Madrid will enter the new year two points clear at the top of La Liga with two games in hand.
#4 Real Madrid end the year on a disappointing note
An excellent run in December had seen Real Madrid win six consecutive games to secure progression in the Champions League and get back into the La Liga title race.
Los Blancos would have sought another victory to end 2020 on a high note but a spirited Elche side stopped them from doing so.
Real Madrid will be hoping to get back to winning ways when they host Celta Vigo in their first game of the new year.