First half goals from French forward Karim Benzema and Portuguese centre-back Ricardo Carvalho helped Real make it a perfect 12 home league wins and keep the pressure on Barcelona in the title race.
It also meant Mourinho extended his personal unbeaten home league run with FC Porto, Chelsea, Inter Milan and Real to nine years with his last league home defeat back on February 23, 2002 when his Porto side lost 3-2 to Beira Mar.
Barcelona, beaten 2-1 by Arsenal in their midweek Champions League match, will hope to respond with a home win over Atletic Bilbao on Sunday to restore their five-point lead at the summit.
"We don't depend on ourselves and really the pressure is on us in second, not on the team at the top," Mourinho said. "I don't know if I will watch Barcelona v Athletic (Bilbao) on Sunday. We are travelling (to Lyon) on Monday so perhaps I will eat out with the family."
Mourinho rested Mesut Ozil, Xabi Alonso, and Emmanuel Adebayor with Tuesday's Champions League match in Lyon in mind, but his side were still too strong for a Levante side they had thrashed 8-0 in the Kings Cup.
"We gave a rest to (Mesut) Ozil and Xabi (Alonso). Everyone knows they will play against Lyon, who have had 24 hours more rest than us," added Mourinho.
With just six minutes gone Argentine di Maria dribbled past three defenders before crossing to give Benzema an easy tap-in for only his third league goal of the season.
Di Maria, Cristiano Ronaldo and Marcelo all went close before Madrid got their second from a set-piece five minutes before the break.
Ronaldo floated in a cross from the left and compatriot Carvalho volleyed home from close range as Levante got their back line all wrong.
Levante, two points above the bottom three, had won their last three league outings but hardly troubled stand-in Real goalkeeper Antonio Adan, deputising for the suspended Iker Casillas, with the 23-year-old having a comfortable game on his Real home league debut.
German international midfielder Sami Khedira had the chance to make it 3-0 early in the second half but didn't get a good connection on his shot and goalkeeper Gustavo Munua saved.
Munua had to be at his best on 64 minutes as he tipped over a header from Ronaldo and then denied Benzema from the resulting corner.
Ronaldo, who could easily have had a hat-trick, was thwarted again in the 80th minute as Real pressed for more.
Earlier third-placed Valencia missed the chance to pull away from Champions League rivals Villarreal following a disappointing 0-0 home draw with strugglers Sporting Gijon on Saturday.
Valencia were in a rich vein of form with six league wins from seven in 2011 but were out of sorts at the Mestalla stadium as they failed to score in the league for the first time since early December.
Valencia stay third but fourth-placed Villarreal can move level on points with a home victory over bottom side Malaga on Sunday.
For Sporting, who drew 1-1 with Barcelona last time out, it was a valuable point and they move two points above the relegation zone.
Valencia, who drew 1-1 with Schalke in their Champions League last 16 first leg match in midweek, looked slightly jaded and Sporting almost won the game in the final seconds with Mate Bilic inches away from connecting with a cross from the left.
In other matches, Atletico Madrid ended a run of four consecutive defeats with a 1-0 win at Real Zaragoza on Saturday to move four points off the top six.
Argentine international forward Sergio "Kun" Aguero scored the winning goal on 65 minutes to relieve the mounting pressure on coach Quique Sanchez Flores.
Zaragoza, who hit the woodwork twice in the closing minutes, hover one point above the bottom three after their 11th defeat of the season.