Cristiano Ronaldo opened the scoring with his 38th goal of the season when he headed Angel di Maria’s corner low past Keylor Navas after just 11 minutes.
Navas then kept his side in the game with a string of fine saves, but there was nothing the Costa Rican could do when Ronaldo teed up Marcelo to curl in the second four minutes after half-time.
Levante were reduced to 10 men on 63 minutes when David Navarro was shown a straight red card for a foul on Ronaldo.
And the visitors’ miserable evening was summed up when Nikos Karabelas’ scored a spectacular own goal nine minutes from time to make it 3-0.
Victory means Real now lead second-placed Atletico Madrid by three points with Barcelona a further point back in third.
“It is a small advantage, but we cannot get ahead of ourselves. We can only think about the next game,” said Real boss Carlo Ancelotti.
“At one point we were six points behind so right now we are in a very good position. All we can do is conitnue in this form.
“There is still a long way in the season to go and the objective is to get to the last game of the season in this position.”
Seemingly buoyed by Barca’s latest setback in losing to lowly Valladolid on Saturday, Real started very brightly and Ronaldo forced Navas into his first stop after five minutes with a nicely cushioned volley that the ‘keeper collected at the second attempt.
The Portuguese wasn’t to be denied six minutes later, though, as he rose highest to meet Di Maria’s cross and power his header low into the corner.
Navas then had to be quick off his line to smother efforts from Di Maria and Karim Benzema as Madrid continued to press.
The pick of the saves from the Levante goalkeeper came in first-half stoppage time as he leapt to his right to turn Benzema’s header from close range onto the post.
Ancelotti’s men did eventually get the all-important second goal four minutes after the restart when a lovely one-two between Ronaldo and Marcelo freed the Brazilian inside the area and he curled the ball into the far corner on his weaker right foot.
Navas continued to frustrate Benzema moments later as he turned away the Frenchman’s fiercely struck effort from the edge of the box.
Levante were reduced to 10 men just after the hour mark when Navarro’s reckless challenge from behind on Ronaldo was deemed to be worthy of a straight red card by referee Ignacio Iglesias Villanueva.
The visitors then inflicted more damage upon themselves nine minutes from time when Karabelas swept home Marcelo’s cross.
However, there was just one moment of worry for Real when right-back Dani Carvajal collapsed to the turf in stoppage time under no pressure from a Levante player and had to be stretchered from the field.