Real coach Zinedine Zidane said Atletico had bossed the first half while his side had edged the second and his team still firmly believed they were in the race.
Benzema has netted 17 goals this season in all competitions for Real, who sit second in the table, six points behind leaders Atletico Madrid having played a game more.
Tomorrow he won't play. He's got something, a problem, that flared up yesterday (Thursday) and he won't take part tomorrow.
French national soccer federation president Noel Le Graet said in a Saturday interview with French radio network RTL that Zidane would be his number one candidate to succeed Didier Deschamps.
We'll see but right now my mind is focused on here. I'm the Real Madrid coach and I enjoy every day of it.
"I don't know if we'll use it again because we have to adapt to whatever situation we find ourselves in, but we did well and I'm happy for the players because what they did today was not easy."
He was more composed in Monday's news conference ahead of Real's home match against Getafe but did not want to discuss whether he would remain until his contract ends in June 2022.
"We'll see about that, the most important thing is how we work each day, that's what I'm concerned with," Zidane said.
“Real Madrid would like to inform that our president Florentino Pérez has tested positive in the COVID-19 tests that he periodically undergoes, although he is not showing any symptoms.”
Perez's positive test comes after Real Madrid coach Zinedine Zidane also tested positive last month.
Hazard made it three four minutes later. Kroos looked up and as Alaves pushed out, Hazard surged in behind, the ball looping over for him to control and finish past Fernando Pachecho.
The French forward got Real off to a flying start by scoring in the sixth minute, trapping a chipped pass from Rodrygo with his right foot and calmly finishing into the net with his left for a fifth goal in his last four matches in all competitions.
Gladbach created little of note and found it impossible to escape Madrid's relentless press, showing few similarities to the side which almost shocked the Spanish champions in the 2-2 draw they shared in October.
"We don't just play well under pressure, we have played well in other games too but it's true that this team has this ability to come into their own when the going gets tough," Zidane said.
La Liga is due to finish on July 19, meaning there will be fixtures every day while clubs will be in action almost every three days for five and a half weeks.
The important thing is the preparation and I think we have prepared very, very well. Our fi