Having opened the campaign with a lacklustre 2-1 victory at Real Betis last weekend, the capital club were indebted to a scrappy Karim Benzema strike at Los Carmenes to make it two wins from two.
The visitors had chances to extend their advantage, notably through Mesut Ozil and Cristiano Ronaldo, and, although no second goal was forthcoming, the Andalusians did not offer much as an attacking force and Madrid took home the points.
Angel Di Maria and Alvaro Arbeloa were handed starts by Madrid coach Carlo Ancelotti, in place of Sami Khedira and Daniel Carvajal, with Diego Lopez retained between the posts ahead of Iker Casillas.
Diego Mainz started in central defence for the hosts in the one change to their line-up from last weekend's 2-1 win at Osasuna, Jeison Murillo the man missing out.
Ancelotti had insisted at his pre-match press conference that there was still room for Benzema despite his desire to move Ronaldo into a more central position, and the France forward - who equalised against Betis - needed only 10 minutes to break the deadlock on Monday night.
Having slashed a right-footed effort into the side-netting after a menacing angled run on four minutes, Benzema tucked home the game's only goal six minutes later. The Granada defence failed miserably in its attempts to play an offside trap and, although Ronaldo miscontrolled Di Maria's cross, it fell kindly for Benzema to prod past Roberto from close range.
The visitors thought they had doubled their advantage on the quarter-hour mark when Ozil dinked a neat finish over Roberto from Di Maria's free-kick, but the goal was disallowed as the referee adjudged the ball was moving at the set-piece.
Ozil was denied again moments later when he burst through only to be denied by Roberto.
Lopez had to be alert at the other end in the 19th minute when Youssef El Arabi found himself unmarked 12 yards out but his weak right-footed shot did not unduly trouble the Madrid keeper.
Having been subdued for much of the first half, Granada started the second looking slightly livelier. Substitute Ivan Riki had a decent half-sight of goal in the 58th minute but lashed over.
The hosts then had shouts for a penalty waved away after the ball appeared to strike Arbeloa's upper-arm/shoulder area.
Madrid too could have added to the scoresheet.
Isco, scorer of the late winner in the lacklustre triumph over Betis, went close to making it two goals in two games in the 62nd minute when he cut inside on the left and whipped in shot which was touched by Roberto onto the base of the post and away for a corner.
Benzema then surged down left only to shunt his left-footed shot well wide in the 68th minute, while Ronaldo muscled his way into a shooting position nine minutes later only to be thwarted by Roberto.
Granada's Argentinian forward Diego Buonanotte went down under a challenge from fellow substitute Casemiro in the closing stages, but the hosts' penalty appeals again fell on deaf ears.
Piti then produced a dangerous stoppage-time cross which required a last-ditch clearance from Pepe, but that was as close as Granada got and Madrid were home and dry.