The hosts had to wait until the 55th minute to take the lead in Madrid, with Granada proving strong opposition.
The result has taken Real Madrid to the top of the table, while Granada are still waiting for their first win of the campaign.
Here, Sports Mole has dissected the 90 minutes of action in Madrid.
On target: 10
On target: 3
Was the result fair?
One look at the statistics would seem to suggest that Real Madrid deserved to claim all three points at the Bernabeu, but the numbers on display do not tell the whole story. Indeed, Granada should have been ahead in the 20th minute when Youssef El-Arabi converted a super cross from Isaac Success, but the flag was raised. Replays showed that it was a poor decision from the linesman and it ultimately cost the visitors the chance of taking something from the match. Real Madrid, as expected, dominated the possession for long spells, but they came up against a goalkeeper in fine form, with Andres Fernandez making save after save to keep the scores level at the interval.
Real Madrid started the second period on the front foot, however, and eventually got their goal 10 minutes after the interval when Benzema headed an Isco cross home from close range. It was harsh on Granada, who themselves had an excellent chance to take the lead through Success moments before. Both teams had chances to add to the scoring as play developed, but Real Madrid were in control for long spells. The home supporters would have a strong case for arguing that their team deserved the points, but Granada's performance will leave them wondering what might have been.
Real Madrid's performance
Without Danilo, Sergio Ramos and Gareth Bale through injury, head coach Rafael Benitez was forced into changes at the Bernabeu, with Lucas Vasquez coming in for his first Real Madrid start. Elsewhere, Dani Carvajal and Pepe started, which was an indication of the strength in-depth that Los Blancos possess. The home side did not really create a chance of note until the 19th minute when Isco found Cristiano Ronaldo inside the box, but Fernandez was down to make an excellent save. Then came the disallowed goal for Granada, which was a real let-off for Real Madrid during an end-to-end period of the contest. Ronaldo, Benzema and Isco were all denied by the away side's goalkeeper in the latter stages of the first period and there was frustration in the stands. Last season, Real Madrid thumped Granada 9-1 in the corresponding fixture and were 4-0 ahead at the break. This time around, however, they were finding it tough.
Indeed, Raphael Varane and Pepe did not look entirely comfortable with the pace of Granada's forward players, but the hosts remained in control of the possession and it did not come as much of a surprise when Benzema opened the scoring. Ronaldo had a personal battle with the Granada goalkeeper as the second period progressed, but the Portuguese could not add to his eight goals in his last two appearances. Denis Cheryshev also came close late on, but Granada just could not find a response down the other end, which made Benzema's header enough to claim all three points. It is difficult to be too critical of a team that had 20 attempts - 10 of which were on target, but they were caught out defensively on a number of occasions and were fortunate to post another clean sheet - their fourth in a row this season. It is another three points in the league, but this performance was not on the same level as the two that preceded it.
Having lost on 18 of their last 21 visits to Real Madrid in the league and taken a 9-1 thumping in this stadium last season, Granada would have been forgiven for dreading their trip to Madrid on Saturday. Under new manager Jose Ramon Sandoval, however, this is a much better team to the one that struggled last season. It did not take long for the visitors to make an impression on the match, with Success, El-Arabi and Edgar Mendez all causing problems in the final third. Skipper Ruben Rochina also took up a number of dangerous positions and the fact that Granada were willing to attack Real Madrid created an end-to-end and exciting contest. Indeed, the first opportunity of the game fell to the visitors, but Edgar could not find Success with a super cross from the left. Without going over old ground, the offside call when El-Arabi found the back of the net really went against them and a goal at that stage would have put a different spin on the contest.
There is no question that they needed their goalkeeper to be in fine form in the first period to keep the scores level, but Benzema's goal in the 55th minute proved crucial. The opener did not stop Granada from causing problems, however, with El-Arabi again coming close on the hour mark during a period where both managers made changes. It was Real Madrid that looked the most likely to add to the scoring late on, but the performance of the visitors cannot be downplayed. They were a threat going forward, while Doria and David Lomban also had excellent games at the heart of the defence. Whether Granada survive this season is not going to depend on their results at places such as the Bernabeu, but more performances of this ilk will breed confidence throughout the squad. The visitors can take a lot from this game.
Sports Mole's man of the match
Andres Fernandez: Granada's on-loan goalkeeper had an excellent game in Madrid. The 28-year-old, who joined from Porto in the summer, won his personal battle with Ronaldo as he stopped the Portuguese with a number of super saves, in addition to denying Isco and Benzema. The Spaniard might have ended the game on the losing side, but it took nothing away from his display, which was fantastic.
An incident that has already been discussed in-depth has to be mentioned in this category. Granada should have been ahead in the first period when El-Arabi converted from close range, but the linesman on call judged the striker to be ahead of the cross from Success. Replays showed that was not the case and the visitors went on to lose the game. It was a shame because it was such a well-worked goal.
As expected, referee Juan Martinez had a busy game in Madrid. While Granada had a goal disallowed, Real Madrid will feel that they should have had at least one penalty. Marcelo and Isco both went down inside the box under firm challenges in the second period, but Martinez was not interested, much to the frustration of the hosts. The official, who issued four bookings, did allow the match to flow in the correct areas, however, which contributed to the overall entertainment. Some good and some bad from Martinez here.
Real Madrid: Los Blancos will attempt to continue their unbeaten start to the new La Liga season when they travel to Athletic Bilbao on Wednesday.
Granada: Next up for Granada is a home match against Real Sociedad on Tuesday.