Real, brimming with confidence after their statement Champions League win at Manchester City midweek, sit comfortably on top of LaLiga on 78 points, ahead of Barca on 70 and Girona on 65
City, in third place, stayed a point ahead of the Merseysiders with a game in hand thanks to Sergio Aguero's equalising goal.
Knocked out of the Champions League by Monaco in midweek, City fell behind when full back Gael Clichy conceded a penalty six minutes after halftime and James Milner scored from the spot against his old club.
Liverpool, who had come into the game more after a slow start, were pegged back 18 minutes later when Aguero scored from Kevin de Bruyne's fine low cross.
De Bruyne then hit a post and Adam Lallana missed badly for Liverpool in an exciting finish.