In the build-up to the game, the visitors were rocked by the news that manager Zinedine Zidane was not going to travel with the team, having tested positive for COVID-19.
Captain Sergio Ramos was also ruled out with a knee injury, having limped out of his side's defeat to Athletic Bilbao last week. He also missed the Copa del Rey defeat to Alcoyano.
Despite the setback, Real Madrid started the game on the front foot and fashioned the best chances in the early part of the match.
A killer through-ball by Luka Modric found Karim Benzema one-on-one with Fernando Pacheco in the 14th minute. However, but the Alaves goalkeeper did well to pull off two spectacular saves in quick succession.
Los Blancos, however, got their breakthrough from the resultant corner-kick. Toni Kross sent in a trademark pristine delivery, from which Casemiro rose the highest to give Real Madrid the lead.
The capital side continued to push forward in search of a second goal and got a breakthrough when a beautiful team move was finished by Karim Benzema in the 41st minute.
Lucas Vazquez won possession back high in the Alaves half. An excellent counter-attack saw Eden Hazard set Benzema up with a dainty backheel from which the Frenchman rifled home just inside the area.
The Belgium international soon got on the scoresheet himself, racing onto a through pass by Toni Kroos and slotting past Pacheco in the second minute of injury time.
Joselu pulled one goal back for the hosts when he headed home a free-kick by Lucas Perez 11 minutes after the restart.
However, Karim Benzema put paid to any hopes of an unlikely comeback with a well-taken goal in the 70th minute.
Here, we shall have a rundown of five talking points from the fixture.
#5 Real Madrid post a comfortable victory after a testing week
The last few weeks have been trying for Real Madrid, with consecutive losses recorded against Athletic Bilbao and Alcoyano.
The latter defeat was particularly embarrassing, as it came against a third division side in the Copa del Rey. To make matters worse, Alcoyano were reduced to 10 men at the start of extra-time and still managed to knock the Spanish giants out of the cup.
Things became worse for the Bernabeu outfit when manager Zidane tested positive for COVID-19. Despite the setbacks, Real Madrid managed to get the job done in the Basque country.
This win over Alaves marks Los Blancos' first win in four games in all competitions, and fans of the club would be hoping that they can build on this to rejuvenate their season.
#4 Eden Hazard plays a starring role for the visitors
It is no hidden secret that Eden Hazard has not exactly performed at the levels expected of him since completing his club-record move to Real Madrid in the summer of 2019.
A combination of poor form and injuries have seen him fail to make a mark at the Bernabeu but against Alaves, he put out one of his better performances of the season.
He showed great ingenuity to set Benzema up for the second goal, while his technique and ability was on full display for his side's third goal.
The 30-year-old was replaced in the 63rd minute for Vinicius Jr, but he departed the field having made a telling impact on the game.
In addition to his goal and assist, the Belgium international had a passing accuracy of 88.9%, while his all-round play was reminiscent of his best days at Chelsea.
There is still enough time for Eden Hazard to make a success of his Real Madrid career, and his performance on the night could him a much-needed confidence boost.