The victory is only Real Madrid's second in six matches and leaves them four points behind Atletico Madrid, who have two games in hand and play Valencia at home on Sunday.
According to Spain's local media, Real Madrid will miss Eden Hazard for at least two weeks.
Real Madrid's night went from bad to worse when Eden Hazard was forced off on 28 minutes after taking a knock, the latest in a long list of injury setbacks for the Belgium star.
Zinedine Zidane praised his side's performance as one of the best this season as Real Madrid closed in on the Champions League last 16 on Wednesday with a 2-0 win against 10-man Inter Milan
Real Madrid announced on Saturday that their star players Eden Hazard and Casemiro had tested positive for coronavirus.
Eden Hazard scored his first goal for Real Madrid in over a year and his team appear to turn a corner as they beat newly-promoted Huesca 4-1 in La Liga on Saturday.
Indicating the 20-year-old Vinicius Junior during a conversation with Ferland Mendy, Karim Benzema said: "He does what he wants. Don't play with him, brother. He plays against us."
With seven games in the space of 21 days awaiting Barcelona, coach Ronald Koeman could elect to give Lionel Messi a breather before the start of the team's Champions League campaign.
Zinedine Zidane confirmed that Eden Hazard is feeling pain again in his troublesome right ankle and will miss Real Madrid's game away at Athletic Bilbao in La Liga on Sunday.
Real Madrid registered an impressive victory over Valencia that reduces their deficit to two points behind Barcelona, who play away at Sevilla on Friday.
Real Madrid secured a 3-1 win against Eibar at the Estadio Alfredo Di Stefano on Sunday.
After scoring Real Madrid's third goal in the 37th minute, Marcelo dropped onto his left knee and raised his clinched right fist into the air.
Eden Hazard was looking beyond Real Madrid to the Euros after undergoing surgery on his right foot in March while some felt Luis Suarez had played his last game for Barcelona after having a knee operation in January.
Roberto Martinez said that there were no complications with Eden Hazard's surgery and that the Real Madrid star is "not far from running again".
Real Madrid did not announce a recovery time for Eden Hazard but his latest setback will be a worry for Belgium boss Roberto Martinez ahead of Euro 2020 this summer.
Real Madrid's nightmare afternoon was made worse by another injury to Eden Hazard, who was forced off in the second half of their 0-1 defeat to Levante.
Eden Hazard's comeback also coincided with Real Madrid conceding twice in a league game for the first time since October, even if they did let in three in the Copa del Rey against Real Sociedad two weeks ago.
Barcelona were beaten 0-1 by Athletic Bilbao at San Mames while Real Madrid lost 3-4 in a seven-goal thriller to Real Sociedad at the Santiago Bernabeu.