Clinical finishing was the difference for Mourinho's men, who claimed their first three points of the new Liga season despite never hitting their usual heightsCristiano Ronaldo scored his 149th and 150th goals for Real Madrid, who dispatched Granada 3-0 at Santiago Bernabeu on Sunday to pick up their first La Liga win of the season.
The Portuguese's milestone was the highlight of a lacklustre performance from Los Blancos, who never seemed to click into top gear.
Ronaldo opened the scoring in the 26th minute in somewhat fortuitous manner and he doubled his side's advantage eight minutes into the second half with a close-range finish, before limping off with a suspected knee injury.
Granada's hopes were put to rest just before the hour mark as Borja Gomez was shown a red card, and Gonzalo Higuain wrapped up matters with a tap in 14 minutes before the end.
Luka Modric was handed his league debut in an advanced midfield role, lining up behind Karim Benzema, who was chosen ahead of Higuain to lead the line.
Granada meanwhile fielded an offensive-minded XI, with Youssef El-Arabi, Juanma Ortiz, Fabian Orellana and Natonio Floro Flores all playing from the start.
Madrid threatened to break through early on, when Jose Callejon was released by Modric on goal, only to see Tono rush off his line to block convincingly in the fourth minute.
The hosts were bossing the midfield and saw plenty of the ball to keep Granada pegged back in their half. However, their positive start did not result in many clear openings, as they struggled to find many gaps in the opposition back four.
Callejon again provided the danger in the 16th minute, whipping in a dangerous cross that Tono claimed bravely just ahead of the onrushing Sami Khedira. But the Granada stopper was far less convincing 10 minutes later, as an unimpressive piece of goalkeeping handed Madrid the lead.
A silky build up saw Callejon collect at the edge of the area, before slipping in the overlapping Ronaldo, who drilled a shot towards the near post that squeezed past the body of Tono.
The hosts had the advantage, but it was far from business as usual with a stubborn test posed by the determined visitors. Chances remained at a premium as Granada, buoyed by their defensive resilience, began to cause a few problems of their own with their speed in transition.
Madrid managed to threaten twice just before the end of the half. First, Benzema volleyed into the side netting after latching onto a Marcelo cross and then a sublime piece of control in the area by Ronaldo saw him manufacture an inch of space, but his shot was smothered easily by Tono.
The home side’s lethargy seemed set to continue into the second half, but they still managed to grab a second goal eight minutes after the restart. Half time substitute Angel Di Maria was the architect, feeding Ronaldo with a well-weighted through ball, and the Portuguese made no mistake once in range for his 150th Madrid goal.
Granada’s chances were virtually extinguished just before the hour mark, as Borja Gomez was shown a second yellow card for cynically taking down Madrid's milestone man, making the visitors’ task that much harder. Xabi Alonso went close from the resulting free kick, but Tono got down in time to make the save.
There was cause for some concern for the home side shortly after though, as a hobbling Ronaldo was summoned to the sidelines and replaced by Higuain.
And the substitute would make his presence felt in the 76th minute, tapping in a cut back from Benzema to put matters beyond any doubt.
Higuain would come close again in the 83rd minute after racing clear, but his lofted finish over the keeper bounced the wrong side of the post.
By that point, the game had long ceased to be a contest and Madrid played out the remaining minutes to pick up their first victory of the new season.