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.
Real have lost twice in La Liga - 2-1 at Getafe and 1-0 at Sevilla - the same number of defeats they suffered in the whole of last season, while arch-rivals Barca have won all five games.
Real Mallorca, Malaga and Sevilla are level on 11 points in second, third and fourth, while Atletico Madrid are a point behind in fifth ahead of their game in hand at Real Betis on Wednesday.
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.
Alvaro Negredo turned the ball into the net from close range to give Sevilla a 75th-minute lead at the Riazor and Ivan Rakitic added a second seven minutes from time when he charged down an attempted clearance by goalkeeper Daniel Aranzubia.
CONCENTRATION, MOTIVATION
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.
Portugal forward Ronaldo, who dinked a shot against the post moments after his goal, now has 152 goals for Real in 152 appearances in all competitions.
"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.
