Lazio midfielder Lucas Biglia cancelled out Luca Toni's opener in the 27th minute before Juan Iturbe's free-kick put Hellas back in front before half-time.
Hellas goalkeeper Rafael pulled off great saves to deny Lazio an equaliser early in the second half before Romulo made it 3-1 in the 63rd minute.
Toni put the result beyond any doubt when he scored his second of the afternoon 12 minutes from time.
The outcome is Hellas' eighth victory out of nine games at home this season and allowed Andrea Mandorlini's side, who gained promotion to Italy's top flight this summer, to leapfrog Inter Milan into fifth place - Inter take on AC Milan on Sunday night.
Lazio, meanwhile, remain winless on the road this season and have dropped to 10th position.
The hosts got off to a perfect start when Toni headed Jorginho Frello's free-kick past Lazio goalkeeper Federico Marchetti in the fifth minute.
Hellas almost doubled their lead shortly after but Marchetti kept out Iturbe's close-range attempt.
Lazio then equalised when Biglia got past his marker and nodded Antonio Candreva's cross past Rafael.
The home side pressed forward more aggressively and took went back in front in the 44th minute.
There was nothing Marchetti could do as Iturbe's powerful free-kick bounced in front of the Lazio goalkeeper and went over his head and into the net.
Lazio reacted and almost made it 2-2 early in the second half but Rafael pulled off a fantastic save to clear Lorik Cana's close-range attempt.
The Hellas goalkeeper was on hand yet again when he kept out Ogenyi Onazi's header following a great cross from Biglia.
Just when Lazio looked more dangerous Hellas gave themselves some breathing space with a third goal.
A fast counter-attack saw Toni's precise cross find Romulo at the far post and he tapped home from close range.
The away defence were again caught off guard in another deadly counter-attack by Hellas that saw Juan Gomez set up Toni in the area and the veteran forward beat Marchetti with a right-footed strike from 12 yards.