Let me remind you that in the previous matches Real made it out with Betis, Eibar and Villarreal, and also played a draw with Las Palmas.
Neymar capped the victory in stoppage time after Suarez passed for Alcacer, who then found the Brazilian alone to tap home.
In the absence of the suspended Lionel Messi, Neymar's underlined his growing status within the Barcelona team by registering his 100th goal for the club in a 4-1 romp at Granada.
Karim Benzema opened the scoring after 31 minutes with a powerful left-footed strike into the top left-hand corner - a stylish first-ever goal against Alaves for the France worldwide.
Benzema's 30th minute strike meant he has now scored against every team competing in La Liga.
For long periods their players looked jaded after long trips during the worldwide break.
Malaysian PM Najib Razak meets TN Governor
Malaysian Prime Minister Najib Tun Abdul Razak was on Saturday accorded a ceremonial welcome at the Rashtrapati Bhawan here. Najib arrived in Chennai on Thursday on his third visit to India since becoming prime minister in 2009.
And it came from the feet of Isco, who fired home from a tight angle after being played in by Cristiano Ronaldo. We know that we can hurt our opponents at any moment.
Deyverson headed over from point-blank range from Theo Hernandez's cross before Mendez passed up the visitors' best chance when he slotted wide when unmarked at the back post. "He is ready and I am very happy for him and that in this final stretch of the season we can count on players who are important and do well".
Alaves were proving the more threatening side, another huge chance going begging when Edgar somehow missed the target with his volley when left completely unmarked by the Madrid defence from Zouhair Feddal's looping left-wing cross.
The Spain global - a shock transfer target for Barcelona - dribbled through the Alaves defence and produced a composed finish for a seventh league goal of the season.
"For example the second goal", Zidane said. "We have to keep working to turn this around".
Ezequiel Garay, Joao Cancelo and a Raul Albentosa own goal boosted Los Che into 13th place with the victory. I'm looking to take advantage of the every minute the manager gives me and I will be really joyful.