The Spain Under-21 international netted two goals of the highest class as a disappointing Russian side were blown away in La Rosaleda, Saviola also scoring for the hosts
The 20-year-old midfielder scored one in each half to ensure an impressive victory, while veteran hitman Javier Saviola also got in on the act with an incisive finish for his new club.
Appearing in their first-ever Uefa Champions League group stage clash after battling past Panathinaikos, the Spanish side made an early statement of their intentions with a goal in almost the first attack of the match.
Great play down the left by Eliseu opened up the Zenit defence, and Isco took full advantage as he left Aleksandr Anyukov for dead before releasing a curling shot past the keeper. With just three minutes on the clock, the Andalusian team had taken a 1-0 lead.
Hulk crashed a shot against the bar to remind the hosts they were still in a match, but Malaga were on a high and soon doubled their lead. Ragged defending and patient build-up play gave Jesus Gamez space on the wing, and his low cross was expertly converted by Javier Saviola to send Malaga into dreamland.
From that explosive start the game developed into an intriguing, high-octane encounter. With less than exemplary work from either backline, both sides had the opportunity to further add to the scoreline. Saviola for one was guilty of squandering a close-range effort after Joaquin expertly turned the beleaguered Anyukov, while at the other end Willy Caballero had to be alert to get down to Aleksandr Kherzakov's snap shot.
Zenit finished the half searching determinedly for the goal that would cut the deficit. Caballero was once again called into action to snaffle Roman Shirokov's header, before a Nicolas Lombaerts effort went just wide of the post.
Both attempts were taken blissfully free of marking from the home side, a warning for Malaga that they would have to tighten up if they wanted to preserve their lead at the end of 90 minutes.
The hosts went within inches of repeating their excellent start to the match in the first few minutes after the interval. Joaquin released Eliseu with a nicely-placed pass, but the midfielder was denied one-on-one by Malafeev when he looked destined to add Malaga's third. At the other end, Caballero was again impressive as he just managed to scoop the ball out of the path of substitute Vladimir Bystrov.
Manuel Pellegrini's men finished the game in buoyant mood, getting behind the Zenit defence at will as the visitors fruitlessly pushed forward in search of a goal. The final nail was driven home with 15 minutes left when Isco netted his second and Malaga's third with a storming strike from the edge of the area. It was no less than the youngster deserved for an all-action performance, and likewise for the Champions League newboys who took home a conclusive, historic victory on their debut.
The win means that the Boquerones go straight to the top of Group C at the end of the first round of matches, after AC Milan were held to a draw by Anderlecht in the other clash. The Spanish side will return to Champions League action on October 3, with a visit to Brussels.