Leonardo's side, who were 2-1 down before racing into a 4-2 lead, remained third in Serie A with leaders Inter Milan and second-placed Juventus also winning over the weekend.
Clarence Seedorf gave Milan an early lead after some neat passing but the Sardinians were ahead on the half-hour after Alessandro Matri and Andrea Lazzari exposed a static defence badly missing the suspended Alessandro Nesta.
The often inconsistent Ronaldinho, who looked refreshed following the international break, hammered in a penalty in the second half to crown another improved display but Milan's nerves were fraught in the closing stages after Nene made it 4-3.
"I've returned to work and felt good. Let's hope I can get a few more goals and we can continue like this," the Brazilian told Sky television.
Juve overcame Udinese 1-0 in a cold Turin in Sunday's late game after Fabio Grosso popped up in the area to guide in fellow fullback Martin Caceres's cross early in the second period.
The hosts, who brought on Alessandro Del Piero for only his second appearance of the campaign after injury, continued their habit of failing to find a killer second goal and were lucky that Udinese were blunted by Antonio Di Natale's suspension.
Francesco Totti had earlier marked his return from almost two months out with a recurring knee problem by scoring a powerful hat-trick in AS Roma's 3-1 home win over Bari.
Walter Zenga's Palermo drew 1-1 at home with his former club Catania in the Sicilian derby and fourth-placed Sampdoria beat Chievo 2-1 in Genoa for their first win in four games.
