Youth team striker Alvaro Morata and Ramos scored inside the opening 12 minutes, but Real were checked when their captain picked up two yellow cards in quick succession to get sent off.
The third-placed champions moved on to 49 points from 24 games, four behind second-placed Atletico Madrid, who remembered how to win on the road again when Radamel Falcao opened the scoring in a 3-0 victory at Real Valladolid.
The match was only three minutes old when Mesut Ozil's low cross found Morata in the area and the 20-year-old fired in the opener.
However, Rayo were let off the hook when Ramos collected two quick yellow cards, first for bundling over a player and the second for a handball after 18 minutes, the 26-year-old Spain defender's 17th red card of his professional career.
"It was a shame because it started so well for the fans," Real director Emilio Butragueno told Spanish television.
"It was difficult to see so it is best not to comment on the referee's decision. The important thing is we won."
Colombia striker Falcao pounced on a loose ball to score after Diego Godin's volley at a free-kick was only parried in the 11th minute. It was his 20th league goal of the season.
Atletico's recent wobble looked to be behind them as they were first to everything and Brazilian striker Diego Costa doubled the lead in the 53rd minute after latching on to a cushioned header from midfielder Koke.
"It was one of our best games of the season," Atletico coach Diego Simeone told reporters. "We were solid, aggressive and intense and the result was never in doubt."
