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The league leader recovered from a goal down in Friday's (AEDT) Copa del Rey defeat of the same side and this time trailed by two, as Lucas Boye and Pere Milla – sent off in midweek – looked set to condemn Madrid to a first home loss in 21 league matches.
Karim Benzema had missed a first-half penalty for the host side, too, but Luka Modric pulled a goal back from 12 yards with eight minutes remaining when Milla was punished for handball.
Militao then headed home a dramatic equaliser in the 92nd minute to deny Elche a first win in this fixture since March 1978 and restore a four-point gap to second-placed Sevilla.