The Qatari-owned club from the Costa del Sol, in their debut Champions League venture, visit Porto in a last-16 first-leg tie on Tuesday.
Argentine Saviola's seventh league goal of the season gave the hosts an 18th-minute advantage. The safe hands of compatriot, goalkeeper Willy Caballero, then helped preserve the lead as fourth-placed Malaga moved on to 42 points.
Manuel Pellegrini's side are four points behind third-placed Real Madrid who host city rivals Rayo Vallecano on Sunday.
Malaga are 20 points adrift of leaders Barcelona who were playing lowly Granada later on Saturday.
Earlier, Getafe made light work of La Liga's worst travellers Celta Vigo, romping to a 3-1 victory with all the goals coming in the first half.
Malaga took the game to Bilbao at the Rosaleda and loan signing from Chelsea, Lucas Piazon, set up the goal for Saviola when he dribbled to the byline and pulled the ball back for the striker to score.
Piazon and Isco were a constant threat in midfield but Malaga were sloppy in defence at times and Caballero had to make a number of sharp saves to deny Bilbao.
The shaven-headed Argentine launched a counter-attack at the end with a punched clearance and Joaquin fired just wide of the post after sprinting the length of the pitch.
Last year's Europa League and King's Cup finalists Bilbao stayed sixth from bottom on 26 points.