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. (Agencies)
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.
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.