The Spanish champions have yet to win on the road this term and suffered surprise defeats at Getafe last month and at Sevilla last weekend. Real lost only twice in securing the league title last season.
Jose Mourinho's men have managed just four points from 12 in the defence of their crown and have slipped eight points adrift of their arch-rivals and leaders Barcelona.
A thrilling fightback to beat Manchester City 3-2 in their Champions League opener on Tuesday has lifted the gloom from the Bernabeu, however, though it required a last-minute winner from Cristiano Ronaldo to secure the result.
"We hope from now on we'll get to see the Real Madrid we all want to see," Spain defender Alvaro Arbeloa told reporters after the City game.
"We are in a delicate situation and we cannot afford any more slip-ups."
Much attention will be focused on whether defender Sergio Ramos returns to the starting line-up at Rayo, after the Spanish international was surprisingly replaced by 19-year-old Rafael Varane against City.
Mourinho said Ramos, one of the leading figures in the dressing room, had been left on the bench on Tuesday for football reasons and not for any disciplinary matter, denying any kind of rift between himself and the player.
Local media had suggested Ramos was singled out for punishment after the Sevilla defeat, when Mourinho launched a scathing attack on the commitment and focus of many of his players.
Rayo, who narrowly avoided relegation last year, saw their unbeaten start to La Liga ended with a 4-3 defeat at Atletico Madrid on Sunday and they lie sixth in the standings, three points ahead of Real.
"Puyol and Pique are major losses but we have players who can step in," Barca midfielder Xavi said after the Spartak game on Wednesday.
Second-placed Malaga visit misfiring Athletic Bilbao on Sunday boosted by their impressive debut in the Champions League on Tuesday when they swept aside Zenit St Petersburg 3-0 at home.
Manuel Pellegrini's side are unbeaten in all competitions since the start of the campaign.