Vialli found the net in the 21st minute to maintain his side's 100 per cent start to the Serie A season, but they struggled to find top form against their newly promoted visitors.
In a remarkable comeback, Lazio fought back from 3-1 down with just 10 men after the 43rd-minute dismissal of their defender Guerino Gottardi. They left Bari, for whom Igor Protti struck a hat-trick, with an unlikely 3-3 draw. Protti, with five goals in three games, is the division's top scorer.
Napoli, who were near to bankruptcy in the close season, continued their revival with a 3-1 victory at previously unbeaten Atalanta.
Sampdoria's dreadlocked Frenchman, Christian Karembeu, found the net twice in his side's impressive 3-0 win over the pre-season title favourites, Parma, for whom the Bulgarian Hristo Stoichkov earned his first Serie A booking - for handing the ball to the referee rather than an opponent.