Los Bermellones now sit in 17th in the table with a record of three wins, nine losses and four draws.
With 21 points Los Leones trail Levante by three for the final Europa League spot, and have compiled a record of six wins, seven losses and three draws on the season.
Athletic Bilbao had 57.3% of possession during the victory.
Los Rojiblancos had 12 shots, including two on target.
Gorka Iraizoz pitched in with four stops.
Mallorca had 42.7% of the possession during the loss.
The Barralets had 18 shots, including four on target.Tomer Hemed had eight shots for Mallorca, more than any of his team-mates.
- Sports & Recreation