Both teams had chances to take the lead in the first period, but impressive stops from each goalkeeper kept the scores level at the interval.
Madrid secured the points in controversial circumstances, however, as Ronaldo slotted a penalty past Javi Varas with 20 minutes remaining.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
CELTA: Varas; Demidov, Tunez, Lago, Johny; Borja, Fernandez, Lopez, Krohn-Dehli; Aspas, De Lucas
REAL MADRID: Lopez; Essien, Albiol, Pepe, Marcelo; Modric, Ozil, Khedira; Callejon, Ronaldo, Benzema