Ronaldo has scored 21 league goals this season but headed into his own net at a corner in the 22nd minute and his side rarely threatened in the face of resolute opposition.
The result left the champions 15 points adrift of leaders Barcelona, who can extend their advantage over their great rivals to 18 with a win at Valencia on Sunday.
Real have 43 points from 22 games and remain four points behind second-placed Atletico Madrid, who host Real Betis on Sunday.
Wednesday's King's Cup semi-final first leg at home to Barcelona, when Real recovered to grab a 1-1 draw, seemed to have taken its toll as Jose Mourinho's side struggled to get going in Granada.
Their hard-running hosts, seemingly inspired by a change of coach from Juan Antonio Anquela to Lucas Alcaraz on Wednesday, took advantage of a familiar failing for Real this season, when they went ahead at a corner.
Ronaldo rose at the near post and skimmed the ball past Diego Lopez and into the roof of his own net.
The visitors slowly found their feet but failed to register a single shot on target before halftime.
Mourinho threw on forwards Karim Benzema and Jose Callejon in a double substitution to try and pep up his team, and Ronaldo became more involved in the game.
The Portugal forward tested goalkeeper Tono on a few occasions but it was Callejon and Benzema who had the best chance between them to level in the 84th.
Callejon dribbled into the area and was denied by Tono, but when the ball broke to Benzema he scuffed his shot wide of the far post in front of an open goal.
Real have lost five games on the road this season and drawn two.
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- Jose Mourinho