Goals from James Rodriguez and Karim Benzema gave them the win that matches the run of Pep Guardiola’s Barcelona side in the 2010-11 season.
Real, without Gareth Bale and Cristiano Ronaldo for the trip to the Cornella-El Prat stadium, made it four wins from four this season.
Barcelona are second on nine points.
Wales forward Bale picked up a hip problem in the 2-1 Champions League win at Sporting Lisbon on Wednesday, while Portuguese star Ronaldo was ruled out with flu.
Colombia forward Rodriguez, who was linked with a move away from the Bernabeu in the summer, scored Real’s opener just before the break.
Receiving the ball from Toni Kroos 30 yards from goal, Rodriguez rode two challenges before shooting low into the corner past Diego Lopez.
Benzema doubled the lead on 70 minutes, meeting Lucas Vazquez’s low cross for a simple tap-in from close range.
The win maintains Real’s unbeaten start to the season and puts them on 12 points, ahead of Barcelona and Las Palmas on nine.
Former Watford manager Quique Sanchez Flores has just two points from his opening four games since taking over at Espanyol in the summer.