Both sides appeared a little rusty after the two-week Christmas break during a tepid first half, but it was Munua who came to the fore in the second to as he saved from Pablo Cendros, Victor and Jose Luis Marti.
Levante failed to create the same number of openings but were also slightly unfortunate as Arouna Kone's goal was ruled out for a very marginal offside decision.
Mallorca manager Joaquin Caparros had demanded a better attitude from his players after their 2-0 defeat to Real Sociedad in the cup earlier this week, and they were the more enterprising side throughout.
Munua had to be quick off his line to deny Emilio Nsue in the best passage of the play in the first half, and Nsue was unlucky not to put the visitors ahead just after the break as his shot flew just wide.
Cendros was next to test the Uruguayan goalkeeper with a fiercely struck effort from the edge of the penalty area.
Munua tipped the ball over the bar before the former Malaga man used his feet to good effect to deny Victor.
Kone was then judged to be offside as he tapped in Asier Del Horno's shot across the box at the back post - replays showing the Ivorian was indeed just a fraction ahead of the last defender.
Five minutes later Marti produced the best effort of the match but again Munua came to Levante's rescue as he somehow got fingertips to the ball to divert the midfielder's free-kick behind.
The point moves fourth-placed Levante to three points behind Valencia who play Villarreal tomorrow, while Mallorca are in mid-table on 19 points.