Zinedine Zidane's Madrid knew that whatever happened in the late fixture they would trail Atletico going into the new year, but they looked on course for a routine win at struggling Elche when Modric opened the scoring in the 20th minute.
Croatian Modric pounced to place a perfect header in the top corner after Marco Asensio's longe range shot thumped back out off the bar, the second time Madrid had hit the woodwork in the early minutes.
The away side thought they had a penalty nine minutes before the break when referee Jorge Figueroa Vazquez pointed to the spot for what he thought was an Ivan Marcone handball, but the awarding was cancelled following a VAR check.
Elche then got a spot-kick of their own five minutes into the second half when Dani Carvajal was caught tearing at Antonio Barragan's shirt, with Fidel stepping up to stroke home the leveller.
Lucas Boye then hit the post for the hosts before home keeper Edgar Badia made two superb stops deny Carvajal and Sergio Ramos as Madrid pushed for a win that would have kept them level on points with their capital city rivals.
"When I look at how we played in the first half, I tell myself it's two points dropped," said Zidane.
"Plenty of teams will drop points. It's a hard season, and we still have plenty of matches left."
December 30, 2020