Their victory, coupled with Madrid’s defeat, means Barca move back to the summit of La Liga, two points ahead of Zinedine Zidane’s side ahead of next Saturday’s showdown at the Santiago Bernabeu.
It amounts to a considerable shift in momentum, with Barcelona away at Napoli in the first leg of the Champions League last 16 on Tuesday.
Madrid host City a day later and the plan had been for Hazard to regain form and fitness in what was only his second start since returning from three months out with a broken foot.
But the Belgian was seen limping and after being taken off he sat in the dugout with what appeared to be an ice pack around the same troublesome right foot.
Madrid were shaken by Hazard’s departure and Levante capitalised as Jose Morales banged a shot into the top corner from the angle, even if Thibaut Courtois pulled out of a save he really should have made.
For Madrid, playing catch-up again next weekend will be a particularly heavy psychological blow, especially given the series of off-field problems engulfing Barcelona in recent weeks.
Real Madrid coach Zinedine Zidane admitted that the injury Eden Hazard suffered on Saturday “doesn’t look good”, four days before their Champions League clash with Manchester City.
Hazard was substituted in the second half of the 1-0 defeat at Levante and was then pictured with an ice pack around the same right foot he broke in November.
“It doesn’t look good,” said Zidane. “It can become weak where you’ve had an injury. It is a blow, let’s see. It’s sore now but we’ll see tomorrow, when we do more tests.”
The Belgian now appears to be unlikely to face City, whom Madrid play at the Santiago Bernabeu in the last-16 first leg on Wednesday.
Since joining Real Madrid from Chelsea last year, Hazard has endured a stop-start season in Spain.
He injured his hamstring the day before Real’s opening fixture in August and then broke his foot in November.
Madrid were never in control of a chaotic contest against Levante but might have taken the lead if Hazard had done better with a long ball over the top from Marcelo, which he failed to control and then scuffed into the hands of Aitor Fernandez.
He limped off and Madrid lost their way, finally punished with 11 minutes left by a straight ball through to Morales. Luka Modric, exposed on the right side of Madrid’s defence, was unable to recover and Morales caught Courtois by surprise by firing early past the goalkeeper and into the top corner.
Real Sociedad moved into fourth and above Atletico Madrid with a 3-0 victory over Valencia, whose miserable form continued following their 4-1 Champions League loss at Atalanta in midweek.