They were driving to a restaurant with friends in the upmarket suburb of Vitacura when their auto was intercepted by the muggers, the Chilean news site 24 Horas reports.
They also recovered a stolen purse but would not confirm it belonged to Ms Pucci.
Local media in the South American nation claim that Pellegrini was approached by the criminals as he got out of his vehicle, with La Cuarta revealing that a purse was snatched before authorities arrived on the scene.
According to a report in the Daily Mirror, the robbers threw spikes on the ground to prevent police from following them after the incident.
The armed robbers were intercepted by police as they tried to run to their vehicle.
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His wife's screams attracted the attention of nearby police officers, who were then shot at by the fleeing muggers, the local police captain said.
No arrests have yet been made.
The owner of the stolen Porsche told local media on Sunday: 'I can't understand how these sorts of things are happening and you can't even go out for dinner without being robbed like this.
The 64-year-old former Man City boss and his wife Carola Pucci were unharmed after being targeted in the Chilean capital of Santiago.
He said: 'Congratulations to @Carabdechile for their speedy and courageous reaction. "Hopefully more faculties will be granted to Carabineros to solve the crime issue as soon as possible".