Following an even start to the encounter, the hosts broke the deadlock in the 33rd minute.
Gonzalo Castro crossed from the right for Casadesus, who headed the ball into the corner of the net from ten yards out.
Chico went close to doubling Mallorca's advantage before the break, but he was unable to convert a pass from Casadesus.
Struggling Zaragoza posed a greater attacking threat after the restart, but they were unable to create any clear goalscoring chances.
The closest they came was when Angel Lafita shot wide of target with 15 minutes remaining.