Franco Vazquez opened the scoring for the visitors early on with his first Serie A goal, only for Luca Toni to level matters with a penalty just before the break.
And Eros Pisano's own goal 13 minutes from the end sealed the points for the home side.
Vazquez broke the deadlock with 18 minutes gone as the forward reacted first to prod home from close range after goalkeeper Rafael had parried Francesco Bolzoni's effort.
But Verona drew level four minutes before the interval as veteran striker Toni scored from the spot having being fouled in the box by Sinisa Andelkovic.
The hosts, who drew their opening game 0-0 against Atalanta, were indebted to a defensive mix-up between Pisano and his keeper Stefano Sorrentino for the points.
Pisano inadvertently nicked a dangerous-looking delivery past Sorrentino and stumbled as he tried to make amends for his error as the ball trickled over the line.