The Champions were without a number of players, which included Marcelo, Toni Kroo and Karim Benzema. While, Gareth Bale was dropped to the bench.
Los Blancos took the lead after 10 minutes as Dani Ceballos managed to work space in the box before firing into the bottom corner. His first goal for the club.
The visitors nearly extended their advantage in the 31st minute but Pacheco produced a superb save to keep out Nacho's close range header.
Alaves managed to pull themselves level with their first real opportunity on 40 minutes courtesy of thumping header from Garcia that sailed into the top corner.
However, Real restored their lead three minutes later when Ceballos bagged his second of the game after a poor error from Pacheco.
The Champions had the chance to extend their lead in the 55th minute when Isco through on goal, but the midfielder failed to convert past Pacheco.
Ronaldo, who was quiet on the night, went agonisingly close to adding Real's third on 64 minutes as his powerful strike crashed against the upright.
The home side nearly leveled matters in the 74th minute as Pedraza rattled the upright with a powerful effort from distance with Keylor Navas well beaten.
Real managed to see out the final 15 minutes with relative ease to claim three points and get the campaign back on track.