Karim Benzema fired Real ahead in the 25th minute with an exquisite first-time finish from a Cristiano Ronaldo cross after Casemiro had begun the move with a clever long ball from the halfway line.
Athletic worked hard to get back into the game and, after Real keeper Keylor Navas produced a brilliant save to deny Inaki Williams, veteran striker Aritz Aduriz headed the home side level from close range in the 65th minute.
Casemiro restored Real's lead in the 68th, however, by controlling a Ronaldo's flicked header from a corner and calmly taking his time to tuck the ball into the net from close range thanks to some careless defending.
Real lead on 65 points from second-placed Barcelona, who have also played 27 games and host Valencia on Sunday.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Richard Martin; Editing by Ken Ferris)
