Ronaldo's fitness has been the source of much concern since an injury-interrupted end to last season and the Portugal international's struggles at this summer's World Cup with thigh and hamstring problems.
However, after Karim Benzema had opened the scoring in Madrid's league opener at the Santiago Bernabeu, Roanldo sealed all three points with a terrific long-range strike in the dying seconds.
Coach Carlo Ancelotti admitted afterwards that the Ballon d'Or holder is not yet in "optimal condition" but Marcelo argued that the 29-year-old does not have to be.
"We know that Cristiano always scores," the defender told reporters after the game. "We trust him and know what he will do for us.
"It is the start of the season and we all have to get better but we gave everything to please the fans. We have the whole league to try and move forward."
The win over Cordoba was Pepe's 250th in a Madrid shirt and the defender was touched by the reception that he received from the home crowd.
"I'm very happy to play so many matches and with the affection shown by the people," the centre-back enthused, "and to help the team to another win.
"We controlled the match well. People were perhaps expecting a more comfortable win but we managed to get three points that are important to us."