The recent international break has left Madrid short of options at the back, with full-backs Marcelo, Fabio Coentrao and Alvaro Arbeloa facing spells on the sidelines, but they attacked from the off although Higuain's 11th-minute opener was a touch fortunate.
Ronaldo netted from the spot midway through the second half to settle matters after Mesut Ozil tumbled in the area following a rather innocuous challenge from defender Gustavo Cabral.
Real No2 Aitor Karanka said: "The back four played very well. Celta only had one header at the end of the match and the back four have played really well. Sergio (Ramos) knew his position; Rafa (Varane) when he plays fulfils his role and Pepe played like he always does."