Barcelona and Atletico had put the pressure on Real by winning 24 hours earlier, but Carlo Ancelotti's men responded with a convincing success away to Getafe to keep pace with the leaders.
Cristiano Ronaldo was serving the second game of a three-match suspension, but it took Real just five minutes to break the deadlock as Jese cut inside from the left and curled a fine finish into the opposite corner for his fifth goal in as many starts.
Karim Benzema doubled their advantage on 27 minutes, firing past Miguel Angel Moya after controlling a pass from Angel Di Maria.
Luka Modric completed the scoring midway through the second half with a low strike into the corner from the edge of the area, before Getafe's fans booed their team at the final whistle as their wait for a first league win since November went on.
Athletic Bilbao's unbeaten league record at their new San Mames stadium came to an end as Espanyol claimed a deserved 2-1 win.
Goals by Sergio Garcia and Diego Colotto ensured Espanyol wrapped up a notable double, having beaten Athletic in September's reverse fixture, and also making it back-to-back league wins after their 1-0 victory over Granada last time out.
Carlos Gurpegi hit Athletic's reply early in the second period but it could not fire the hosts to an improved overall performance and Colotto duly made them pay with the winner after 65 minutes.
Piti scored a crucial goal for Granada as the Andalusian side beat local rivals Real Betis 1-0 to ease their Primera Division relegation fears while adding to those of their opponents.
In a bad-tempered clash which saw both teams finish the game with 10 men, Piti claimed the winner just after the half-hour mark.
Granada's Dani Benitez was shown a straight red card with 10 minutes to go and Antonio Amaya picked up a second yellow card in the dying minutes in a match which saw referee Jose Antonio Teixeira Vitienes show a total of nine yellow cards as well as the two reds.
Just outside the European places, Sevilla and Valencia played out a goalless draw in the day's late game.
Ivan Rakitic missed a penalty on the hour mark and there were red cards on both sides - Valencia's Ricardo Costa in the 50th minute and Sevilla's Denis Cheryshev at the death.