Karim Benzema beat a poorly constructed Rayo offside trap to score the only goal of the game in the 13th minute and Toni Kroos came close to doubling Madrid's advantage later in the first half when he struck a post from outside the box.
The win put Santiago Solari's side up to third place in the standings on 29 points, one clear of fourth-placed Sevilla who host Girona on Sunday and two behind champions and leaders Barcelona, who visit Levante, and Atletico Madrid.
Madrid, who were also booed off on Wednesday after losing 3-0 to CSKA Moscow, their worst-ever home defeat in European competition, continued to suffer defensively at the back.
They leaked plenty of chances to their neighbours, who are fighting relegation and have won only twice all season.
Rayo defender Emiliano Velazquez came close to equalising with a bullet header from a corner shortly after Benzema's goal.
Then, as the visitors laid siege to Madrid's goal in the closing stages, it took an impressive double save from Thibaut Courtois in stoppage time to prevent Rayo from grabbing a point.
Even though the European champions weathered the storm, it did not stop the infamously demanding Santiago Bernabeu crowd from booing their team.
It was a far from ideal send-off in their final league game of 2018 before they fly to Abu Dhabi to defend their Club World Cup title.
Despite the frantic ending and the home fans' angry reaction, Madrid coach Solari said he was happy with his side's performance, adding that the team would travel to Abu Dhabi in good spirits.
"We're feeling very good, we have won nine games out of 11 (since he replaced Julen Lopetegui), we've cut the gap with the teams at the top, we finished first in our Champions League group, we're still in the Copa del Rey and now we're going to a tournament which makes Madrid fans very excited," he said.
The coach dismissed fitness concerns about Benzema and Marco Asensio, who were substituted in the second half, saying he thought both players had only sustained knocks.
(Reporting by Richard Martin; Editing by Ian Chadband and Clare Fallon)
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