Rodrygo continued his impressive scoring streak with his seventh goal in his last five Real appearances to seal victory at the Bernabeu following Brahim Diaz's first-half opener.
It means Real are now tied on 38 points with Girona at the top after Cristhian Stuani's late brace saw the latter beat Valencia 2-1.
Hugo Duro gave Valencia the lead and they looked set to see out the win, but Stuani levelled in the 82nd minute before completing the comeback by scoring the winner six minutes later.
Osasuna and Real Sociedad settled for a 1-1 draw, while Athletic Bilbao moved into fifth in the table after beating Rayo Vallecano 4-0.
Gorka Guruzeta put them ahead in the first half and they extended their lead after half-time when Alfonso Espino turned the ball into his own net before brothers Inaki Williams and Nico Williams struck in quick succession.