The Gialloblu controlled possession and territory early on, with Liovrno happy to break with pace on the counter as a pattern was established early on.
Livorno forced Verona's Rafael to make a superb save with the first clear-cut opportunity of the match, with the goalkeeper turning Paulinho's fierce drive away.
Verona took the lead against the run of play four minutes before half time thanks to Juan Manuel Iturbe, who won a free kick and took it itself, floating a measured effort into the top corner.
Livorno were undeterred and equalised in first-half stoppage time, as central defender Leandro Rinaudo was left unmarked to head home a corner kick from close range.
Both sides then tightened up in the second half, with the decisive moment coming 16 minutes from time as Luca Toni won a penalty for the hosts.
Jorginho stepped up to take the spot kick, sending the goalkeeper the wrong way to make sure that Verona maintained their early 100% home record.