A spate of positive Covid tests prompted coach Carlo Ancelotti to bring Hazard in from the cold yet his team could not find a way through against a determined Cadiz side at the Santiago Bernabeu.
The stalemate reduced Madrid's lead at the top of La Liga from eight points to six at the end of the weekend, after second-placed Sevilla snatched a late victory over Atletico Madrid on Saturday.
Three straight league defeats means Atletico, the defending champions, are now 14 points off the top while Barcelona, who beat Elche on Saturday, are seventh, 16 points adrift.
Hazard's last start for Madrid had come in the humiliating Champions League defeat by Sheriff Tiraspol on September 21th, with the Belgian's season again interrupted by injury and a lack of fitness.
But form has been a key factor too, after Ancelotti stated clearly he "prefers other players" while admitting Hazard would have to show patience and perseverance to earn back his place.
Hazard could even depart as early as January if a significant bid arrived but this was an encouraging night for the 30-year-old, who made little impact from the right wing in the first half but improved immeasurably when moved more centrally in the second.