Joaquin was the hero for the Andalusians, atoning for an earlier penalty miss with the only goal of the game in the second half, as Milan's season goes from bad to worse
The Andalusian outfit has three wins out of three, and remains the only side in this seeason's competition yet to concede a goal after a comfortable victory over the beleaguered Italians, who see more pressure heaped on coach Massimiliano Allegri after another disappointing result.
The scoreline could have been greater had Joaquin not missed a first-half penalty, but the Spanish winger made amends just past the hour mark as he scored the only goal of the game with a cool finish.
Malaga now has nine points from its opening three games in Group C, and holds a five point lead over Milan, which is now looking over its shoulders at Zenit St Petersburg, only a point behind.
With Nigel De Jong sidelined through injury, Massimo Ambrosini was handed his first Champions League appearance of the season, while Alexandre Pato continued his return from a long injury layoff with a place on the bench.
Malaga, facing an Italian side for the first time in its history, carried the momentum of the first half as the play of Joaquin and Manuel Iturra in particular kept Milan perpetually on the back foot.
Milan would slowly grow into the game though, and it managed to fashion the first real chance of the match on the half hour mark, as Urby Emanualson broke free down the right and teed up Stephan El Shaarawy inside the area, who fired over from a great position.
Malaga would hit back soon after, as a slick combination between Joaquin and Isco resulted in the latter bending a shot inches over the bar from the edge of the box.
With two minutes to go until halftime, the home side was presented with a golden opportunity to take the lead, after Kevin Constant tugged down Jesus Gamez just inside the area to concede a penalty.
Joaquin took responsibility from 12 yards out, but over-hit the spot-kick, which clipped the crossbar on its way out of play.
The match remained finely poised as the second half unfolded, but Malaga continued to shade matters, and Saviola nearly had a one-on-one after latching onto Isco’s brilliant cutback, but a superb tackle by Daniele Bonera halted him at the last.
With 64 minutes gone, however, Malaga would finally find a way through. Iturra was the architect, clipping a perfectly-weighted pass over Francesco Acerbi, from which Joaquin needed no second invitation to slot into the corner.
Eliseu nearly added a second moments after the restart when he lashed towards goal from 20 yards out, but the fingertips of Amelia denied him a great goal.
Milan launched a late and desperate charge during the final minutes. El Shaarawy saw a close range shot pushed away by Caballero, and Mexes fired wide after attacking in a good position from the resulting corner.But there was nothing more to come from the Italians, as Malaga held on for a deserved victory, and now sits within touching distance of the knockout stages, while Allegri faces fresh speculation over his future.