In their last four trips to the Estadi Ciutat de Valencia, Madrid have won just once, although that came last season courtesy of a 2-1 triumph, which was sealed by a late Alvaro Morata goal.
Prior to that, Real had not won - or even scored - on their previous three trips to face Levante.
A win will hold even bigger significance for Carlo Ancelotti after last week's 1-0 reverse at home to Atletico Madrid, Real's first league defeat of the 21st century to their city rivals.
The game also marked Raphael Varane's first appearance since suffering a knee injury against Espanyol in May and the France international, who also earned a recall to Didier Deschamps' national squad, was delighted to return.
He said: "I'm very happy. I went a long time without playing and I was on the pitch for the entire 90 minutes which was a real pleasure.
"I worked very hard over the past few days in order to achieve this.
"I feel physically quite good and from now on I hope to play well."
Varane's comeback is a timely boost, with Pepe's availability uncertain after he suffered a nasty head cut against the Danish side.
Since then, Joaquin Caparros' side have drawn four games and won twice, leaving them ninth in the Liga table with 10 points.
