Federico Balverde opened the scoring at the Mestalla after 28 minutes.
Arda Guler was on target with 36 minutes played and Kylian Mbappe completed the rout with his effort with 75 on the clock, before Valencia were reduced to 10 men with the dismissal of Jose Gaya (79').
The result lifted Real to 30 points from 12 games, while Barca have a game in hand against Atletico Madrid on Sunday.
Espanyol and Deportivo played out a goalless draw at the RCDE Stadium to end in 13th and eighth place respectively with 15 and 12 points apiece.
Elsewhere, Athletic Club were held to a 1-1 draw with Osasuna, with Alejandro Catena's (90') stoppage-time equaliser cancelling out Nico Williams' 84th minute effort at El Sadar Stadium on Saturday.
The result left Athletic in seventh place on the league standings with 16 points from 11 games and Osasuna down in 15th with 12 points from 12 games.
And Malaga's woeful season continued with a 2-1 loss to Racing Santander at home.
Carlos Dotor opened the scoring for the bottom placed side after 28 minutes but second half goals from Iker Luque Sierra (50') and Yassir Zabiri (60') turned the tie in Santander's favour.
Malaga sit rock bottom of the standings with five points from 12 games, while Athletic are in seventh with 16 points from 11 matches.
All Saturday's LaLiga results
Valencia 0-3 Real Madrid
Espanyol 0-0 Deportivo
Osasuna 1-1 Athletic
Malaga 1-2 Racing Santander
France have suffered further injury setbacks ahead of their upcoming Nations League fixtures, with Inter Milan forward Marcus Thuram and Real Madrid midfielder Aurelien Tchouameni both ruled out.
Ibrahima Konate has backed Kylian Mbappe to put his recent disappointments behind him, insisting the France captain is in a good frame of mind ahead of his return to international football.
Barcelona produced another impressive comeback to strengthen their position at the top of La Liga, beating Atletico Madrid 2-1 thanks to a Fermin Lopez brace.
Real Madrid manager Jose Mourinho believes Cristiano Ronaldo has plenty left to offer football despite the forward announcing his retirement from international duty.
