Captain Lorenzo Insigne curled in a free-kick after half an hour, celebrating his goal by holding up and kissing the No. 10 jersey of the Argentina legend, who died aged 60 on Thursday (AEDT).
"It's sure these days after Maradona's death have given us an extra boost, our idol has passed away and it hurts," said Insigne.
"Today we wanted more than usual to perform and get a result, for him and for the whole city that is suffering. We dedicate the victory to him."
Napoli's jersey with white and light blue vertical stripes, was specially designed to pay tribute to Napoli's legendary number 10 who led the club to their only league titles in 1987 and 1990 and the UEFA Cup in 1989.
Insigne said: "Tonight's game must be a starting point, if we play like this we can beat anyone.
"Head down and work, we can do great things."
Players also wore black armbands, with a minute's silence observed before the game, as in all matches in Italy, in memory of Maradona who spent seven years at Napoli.
A photo of the former Argentina star was projected onto giant screens in the 10th minute, as players stopped to applaud.
Fabian Ruiz added a second just after an hour with club record goalscorer Dries Mertens slotting in a third with 10 minutes to go.
Substitute Matteo Politano added a fourth with a solo run through the Roma defence four minutes from time as the side from the capital fell to their first away defeat this season.
Napoli, which had lost two in a row at home, overtook Roma to move fifth in Serie A, with both teams equal on 17 points after nine games.
AC Milan is top of the table with 23 points after extending their unbeaten run this season by winning 2-0 against Fiorentina.
The launch of Napoli's new jersey had already been planned before Maradona's death, the club said.
"A year ago, together with Kappa, we thought of designing a special jersey that echoes Diego Maradona, his beloved Argentina and the very strong bond with the people of Naples," Napoli said in a statement.
"Together we hoped that Diego could see it, maybe wear it and share in the excitement with us."
"The shirt that will be worn by the players... will have an even greater significance than initially assumed," it added.
On Friday (AEDT), Napoli players took to the pitch wearing Maradona's iconic number 10 jersey before their 2-0 Europa League win over Croatian side Rijeka.
The Stadio San Paolo is expected to soon be renamed after the 1986 World Cup winner following a suggestion made by the Mayor of Napoli.