Cristiano Ronaldo, the leading scorer in Spain this season, took his tally to 24 goals when he headed the opener from Angel Di Maria's corner in the 11th minute and Marcelo added a second from Ronaldo's assist four minutes after the break.
David Navarro was harshly shown a straight red card in the 64th minute for an innocuous-looking tackle on Ronaldo and fellow Levante defender Nikos Karampelas put the ball into his own net nine minutes from time.
Ronaldo, who became Portugal's leading scorer with a double against Cameroon in Wednesday's 5-1 friendly victory, came close to a second in the 90th minute when he headed against the underside of the crossbar and Gareth Bale whistled a low shot just past the post in added time.
"I don't think it was a perfect game but we were close," Marcelo said in an interview with Spanish television broadcaster Canal Plus.
"We were a bit weaker in the first half than the second but the important thing was that we didn't concede any goals and in that respect we have improved a lot," added the Brazil international.
"We couldn't afford to stumble today and of course it's better when the others lose but we are focusing on ourselves."
Real, unbeaten in 29 matches in all competitions, have 67 points with 11 matches left and Atletico Madrid are three behind in second after they won 2-0 at Celta Vigo on Saturday.
Champions Barca, who play at Real in the La Liga "Clasico" in two weeks time, turned in one of their worst performances of the campaign on Saturday at Valladolid, who are battling relegation, and slipped to third on 63 points.
Seventh-placed Sevilla boosted their chances of qualifying for Europe again this season with a 3-1 win at Almeria, while mid-table Espanyol stayed in the hunt for a place in continental competition with a 3-1 success at home to Elche.
Fourth-placed Athletic Bilbao can move nine points clear of Villarreal, who lost 2-0 at Granada on Saturday, with a win at Valencia later on Sunday.