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.
World Player of the Year Ronaldo restored the lead with a penalty won by Raul and after Deportivo had again levelled, a long range drive from Lassana Diarra sealed victory.
"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."
Real, beginning their campaign to wrest the league title from treble-winners Barcelona, started briskly, with Brazilian playmaker Kaka looking particularly dangerous.
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.
GOOD FEELING
Depor stunned Real with a second equaliser immediately after the restart. Mexican midfielder Jose Guardado picked out Juan Carlos Valeron on the edge of the area and he drilled a superb shot low past Casillas.
Diarra grabbed the winner on the hour when he rounded Juca and found the far 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.
The 80,000 spectators at the Bernabeu gave world 100 and 200 metres champion Usain Bolt a huge ovation when he came on to the pitch before kickoff and showed off some ball skills.
