The Portuguese winger was a threat to the visitors' defence all afternoon and showed great skill to open up a shooting chance for himself before firing low past Dudu Aouate in the 30th minute.
Gama and Pizzi also hit the woodwork for the hosts in the second-half but despite a late flurry of long-range efforts from Mallorca they held on to move out of the bottom three.
Theses sides had already met earlier in the week, drawing 1-1 in the first-leg of their Copa del Rey tie, but in contrast to that match it was Mallorca who started the brighter.
Michael Pereira was keen to impress after being dropped for the defeat to Real Madrid last weekend and he forced Daniel Aranzubia into an early save before dragging another effort from outside the area just past the post.
Yet it was the hosts who went ahead with their first serious effort of the game as Gama picked the ball up on the right and cut inside before leaving two defenders on the floor as he turned back onto his favoured right foot and smashed in his first goal of the season.
Javier Arizmendi had a great chance to bring the visitors level three minutes into the second period but could only fire straight at Aranzubia after latching onto an error by Pedro Geromel.
Instead it was Depor who came closest to scoring again after the break as Gama was unlucky to see his clever lob over the stranded Aouate come back off the post before Pizzi fired a free-kick against the crossbar.
Substitute Marc Fernandez forced Aranzubia into another comfortable save 25 minutes from time and Giovani Dos Santos curled a free-kick in a dangerous position inches wide in stoppage time.
But Mallorca could not find the breakthrough they needed to avoid a fifth consecutive league defeat.