Goals from Adem Ljaljic, Gervinho and Francesco Totti handed the away side the points as Emil Hallfredsson's second-half equaliser proved not enough for Verona.
The Giallorossi recorded a 1-0 victory over Juve in the Coppa Italia in midweek and made it their fifth win in succession, condemning Verona to their third straight league defeat.
Rudi Garcia's visitors started well and could have taken an early lead as Maicon's cross in the box almost got deflected into the net by Verona defender Fabrizio Cacciatore before goalkeeper Rafael blocked his effort on the line.
Serbia midfielder Ljajic had a couple of good chances to hand his side the lead but the first was kept out by Rafael and his second went over the bar.
Roma finally got on the scoresheet in first-half stoppage time as Ljaljic picked up Gervinho's cross from the left wing and made no mistake as he slotted home from close range with his fifth goal of the season.
The home side hit back just minutes after the break as Juan Iturbe made his way down the pitch, finding Massimo Donati, who crossed the ball into the box for Hallfredsson to make it 1-1.
But on the hour mark Roma took the lead for the second time as provider Gervinho scored from a corner as he got the ball in the back of the Verona goal from close range.
The visitors continued to press forward in search of another goal and that came in the form of a penalty in the final 10 minutes after Alejandro Gonzalez brought down Vassilis Torosidis inside his own area.
Totti made no mistake, firing the ball with his right foot in the bottom left corner with Rafael well beaten.
Romulo had a chance to pull one back for Verona minutes later but the Brazilian shot just wide of the post.