Real spent 250 million euros over the close season, including a world record fee of over 90 million euros to sign Ronaldo from Manchester United, and despite twice squandering the lead they made a winning start to their new era.
Raul opened the scoring after some clever work from Kaka, another of their big-money signings, only for poor marking to gift Deportivo their first equaliser.
"Expectations are always very high and the nerves and pressure were having an effect throughout the match," new coach Manuel Pellegrini said.
"But we scored three goals and had many more very clear chances. We dominated the match and for the first game of the season the team put in a solid performance."
His pass in the 26th minute should have been cleared but the ball fell to Karim Benzema and Raul was on hand to tap in the rebound when the Frenchman's shot came back off a post.
Riki was left unmarked four minutes later to head Juca's deep cross past Real goalkeeper Iker Casillas before Raul was felled by Depor keeper Daniel Aranzubia and Ronaldo stroked the resulting 35th-minute penalty into the bottom left corner.
"The first match is always the most difficult but the feeling was very good," Ronaldo told reporters.
"There were good things and some bad things that we need to fix," he added. "We will carry on improving bit by bit."
Barcelona's opening match against Sporting Gijon has been put back to Monday because of the champions' European Super Cup match against Shakhtar Donetsk on Friday, which they won 1-0.
