A fine finish from Vinicius and Sergio Ramos' brilliant second-half free-kick saw Madrid climb back above rivals Barcelona and to the top of the LaLiga table.
Vinicius was happy with his performance and also talked up his combination with Hazard, with the pair starting together in Madrid.
"I am very happy with today's match. We have worked a lot at home to get to our best version," the forward said, via the club's website.
"As for me, I think I'm the same as before the break, but it's true that I worked a lot at home to be physically well.
"This is like a World Cup with few games and we have to be focused from the beginning. I always try to improve in all aspects. The coaching staff always helps me a lot to improve and I want to continue evolving at Real Madrid.
"Hazard is easy to play [with] because he is a great player and today was the first time that [Zinedine] Zidane has brought us together. It went very well."
Madrid extended their winning streak to four since returning from the coronavirus-enforced break, staying on track to win the LaLiga title.
Vinicius said it was important for the whole squad to be ready when called upon by head coach Zidane.
"We are all ready to enter the field when Zidane decides and we will do our best. We have the best players on the field," he said.
"We are going to do our best to win the remaining seven finals. We have won four and we are going for the league."
Madrid continue their campaign with a trip to Espanyol on Sunday.