The result was also the perfect morale-booster for the Andalusians ahead of their Champions League last-16 first-leg tie against Porto next week.
Malaga coach Manuel Pellegrini did not appear to have the Porto game in mind at the Rosaleda, because he sent out an almost full-strength team, only resting Joaquin and Jeremy Toulalan, who began the game on the bench.
Despite the low scoreline, the game saw plenty of chances created by two teams committed to playing creative, attacking football for the whole 90 minutes.
Marcelo Bielsa named 20-year-old goalkeeper Raul in his starting line-up in place of Gorka Iraizoz, who conceded four goals against Espanyol last weekend and was booed by the San Mames crowd for his poor performance.
However, it was the Malaga goalkeeper Willy Caballero who stole the show with a number of outstanding saves to keep out Bielsa's side.
Lucas Piazon, on-loan from Chelsea until the end of the season, made his first start for Malaga and marked the occasion by providing the assist for the only goal of the game.
The 19-year-old used skill and strength to advance into the Athletic area and pulled a pass back from the by-line into the path of Saviola near the penalty spot and the striker shot high into the net on 18 minutes.
Caballero produced an outstanding double save to deny Aritz Aduriz a goal in the first half and then performed more heroics to keep out three efforts from Ibai Gomez in the second period.
Athletic had the ball in the net on 77 minutes, but Fernando Llorente was ruled offside in the build-up and the goal was not allowed to stand.
Substitute Joaquin missed a glorious chance to double the lead in stoppage time but put his shot wide, while Isco had a goal-bound shot blocked just before the referee blew the final whistle.