Karim Benzema finished off a swift breakaway 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.
The victory, only their second success in five games this season, lifted Jose Mourinho's side to seventh on seven points, eight behind leaders Barcelona, who were 2-0 winners at home to Granada on Saturday.
Real have already lost twice in La Liga - at Getafe and Sevilla - the same number of defeats the champions suffered in the whole of last season, while arch rivals Barca have won all five of their games.
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.
"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."
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