Goals from Fabrizio Cacciatore and Juan Iturbe gave the visitors a commanding 2-0 half-time lead at the Stadio Renato Dall'Ara.
Alessandro Diamanti pulled a goal back from the penalty spot shortly after the restart, but Luca Toni swiftly restored Verona's two-goal cushion before Jorginho Freiro sealed matters in stoppage time.
The result continued Verona's impressive start to the campaign, with the promoted outfit having taken 13 points from seven games.
Bologna, meanwhile, remained without a win and headed into the international break in 19th place in the standings.
The hosts went into the game looking to make amends for their 5-0 defeat at Roma last time out.
The encounter started 20 minutes late after the police had to disperse a number of Bologna fans attempting to clash with rival supporters outside the ground.
Verona dominated possession early on and went ahead midway through the first half when Juan Gomez fed Cacciatore in the box and his powerful effort beat Bologna goalkeeper Gianluca Curci.
Bologna had little time to react as Verona struck again seven minutes later, Iturbe's stinging drive from 30 yards finding its way past Curci.
The home team should have reduced the deficit before half-time but Panagiotis Kone's shot from just outside the area was kept out by Verona goalkeeper Rafael.
Bologna were given a helping hand in the 52nd minute when the referee pointed to the penalty spot after Alejandro Gonzalez was brought down by Davide Moscardelli in the box.
Diamanti stepped up and slotted his left-footed spot-kick past Rafael to give the hosts hope of getting back into the game.
But Verona extended their lead four minutes later when Iturbe found an unmarked Toni in the box and his 10-yard shot got the better of Curci.
With seconds remaining, Verona rubbed salt in the Bologna wounds by making it 4-1. Romulo set up Jorginho, who lashed home a right-footed strike to round off the rout.