Karim Benzema scored the only goal as Real Madrid were made to sweat to see off a bold Granada side at the Bernabeu.
The Frenchman headed in a cross from Isco nine minutes into the second half to break the deadlock against the dogged Andalusians, who had what looked to be a legitimate goal ruled out for offside and squandered a number of clear scoring chances.
Cristiano Ronaldo was unable to add to the eight goals he had scored in his last two matches and will have to wait at least until Madrid's trip to Athletic Bilbao on Wednesday to become the club's all-time top scorer.
Injuries to Gareth Bale and Sergio Ramos in the 4-0 win over Shakhtar Donetsk in midweek forced Rafa Benitez to recall Pepe to defence and hand Lucas Vazquez his start for the club.
Granada were thrashed 9-1 here last season, but the Andalusian side appeared to have learned the lessons from that day and coach Jose Ramon Sandoval employed an intelligent game plan based on deep defending and purposeful counter-attacking.
Their approach meant Madrid did not create a clear opening until the 20th minute, when Isco played in Ronaldo, Andres Fernandez saved the Portuguese's shot and the ball dropped to Vazquez, who flashed the rebound well wide with the goal gaping.
Granada went straight down the other end and thought they had taken a shock lead when Youssef El Arabi passed a low cross into the net, but the Moroccan was harshly ruled offside.
Madrid recovered from this scare and grew in confidence. Fernandez spilled a free-kick from Ronaldo but got up in time to save Vazquez's attempt on the rebound with his shin, and on the half-hour mark the goalkeeper saved a stinging effort from Luka Modric with his feet.
Isco then flashed a shot just wide of the far post, which an anguished Ronaldo was inches away from connecting with. The Portuguese also narrowly failed to get on the end of a cross from Benzema a minute before the break.
At the other end, Granada striker Isaac Success was denied by the quick reactions of Madrid goalkeeper Keylor Navas, and the visitors continued to play well in the second half.
They had another chance to break the deadlock when El Arabi's back-heel released Success, but the Nigerian's attempt to lob Navas went over the bar.
Madrid made Granada regret their wastefulness swiftly, as Isco's hanging cross from the left was headed home at the far post by Benzema.
El Arabi could have levelled shortly afterwards but failed to get his shot away in time, and Navas was able to block the effort.
Ronaldo had been relatively quiet by his standards in the game but came to life midway through the second half, forcing Fernandez to tip over a long-range effort, and then struck just wide of the the far post with his left foot.
He was denied the opportunity to score from the spot as the referee refused to give what looked a clear penalty when El Arabi sent Isco tumbling in the box, and will hope for better luck when he and Madrid take to San Mames next week.
Source: PA
