Karim Benzema finished off a swift breakaway from an Angel di Maria pass in the 13th minute and Xabi Alonso had to clear a Rayo effort off the line before Cristiano Ronaldo netted from the penalty spot 20 minutes from time.
Only the second win for Jose Mourinho's side in five games this season lifted them to seventh on seven points, eight behind leaders Barcelona who beat Granada 2-0 at home on Saturday.
Sevilla won 2-0 at promoted Deportivo La Coruna in Monday's late kick-off after Mallorca beat Valencia 2-0 and Malaga ground out a 0-0 draw at Athletic Bilbao on Sunday.
Mourinho was sharply critical of his players after the surprise reverses at Getafe and Sevilla, accusing them of lacking focus, and he dropped Spain centre back Sergio Ramos for last week's Champions League victory at home to Manchester City.
Ramos was back in the starting line-up on Monday and Real appear to have turned a corner after flirting with crisis following last weekend's defeat in Seville.
"If we had played with a similar attitude against Getafe and Sevilla [as we had tonight] we would have won those games," Mourinho told a news conference.
"It was a tough game, a difficult game and we had to be at the least at our best in terms of concentration and motivation and it seems that the team responded well in that sense," added the Portuguese.
"Could we have played better? Yes, we could have played better even though our opponent pressured a lot and ran a lot and caused us problems.
"But my criticisms are always directed at my players' attitude and whether they are committed to the game and today the team was a team."
Monday's match had been due to be played on Sunday night but was postponed because of alleged sabotage to the lighting at Rayo's Vallecas stadium.
