Joaquin's 64th-minute strike at the Rosaleda on Wednesday secured a memorable 1-0 win for the Champions League debutants, who after three wins in as many matches sit at the top of Group C with a five-point lead over the ailing Italians.
The home fans thronging their 29,500-capacity stadium for what was probably the biggest game in the La Liga club's history, thoroughly enjoyed their first taste of life among Europe's soccer elite.
It was a far cry from the uncertainty of the close season, when reports Qatari owner Sheikh Abdullah Bin Nassar Al Thani was looking to sell up after only two years went unanswered, some of the team's best players moved on and those left behind were not paid on time.
Al Thani eventually let it be known he was not seeking an exit and the club announced it was going through a process of "internal restructuring" to make it more financially viable.
Results on the pitch have been impressive despite the instability and Manuel Pellegrini's side are within touching distance of a place in the Champions League knockout round.
They are third in La Liga, five points behind leaders Barcelona and Atletico Madrid, and Pellegrini has managed to mould his squad into a side that is dangerous on the attack and mean in defence.
Al Thani, a member of the Qatar royal family, showed up for Wednesday's game, his first appearance at the stadium this season, and told Spanish television in a brief post-match interview there would be more money available.
"Of course we are going to invest, there is a future," he said. "I congratulate the players, the coach and above all the fans for their support."
Pellegrini, who was fiercely critical of the club's management over the summer, said it was important Al Thani had come to the match.
"He came into the dressing room and greeted everyone," the Chilean told a news conference. "Now we can talk about other things."
Malaga have a chance to prove Wednesday's result was no fluke when they play at Milan on Nov. 6. Their final two matches in the four-team group are away to Zenit St Petersburg on November 21 and at home to Anderlecht on December 4.