The Brazilian playmaker, signed from Werder Bremen in the close season, demonstrated why Juve fans hope he is the missing link to bridge the gap with champions Inter Milan this term.
"It's thanks to the environment at Juve, coach Ciro Ferrara, my team mates and the fans that I've settled in so well," Diego told Sky television.
Having produced flashes of brilliance in last weekend's 1-0 win over Chievo in Juve's league opener, Diego netted his first competitive goal for the club midway through the first half.
Roma's Daniele De Rossi equalised for the hosts 10 minutes later and although different, his goal was equally breathtaking.
Diego was not to be outdone, however, and he ran on to Vincenzo Iaquinta's clever flick in the second half and bamboozled the Roma defence before rifling home.
Fellow Brazilian Felipe Melo, another big money buy from Fiorentina, sealed Roma's second league defeat with a fierce strike in injury time having struggled for much of the match.
Juve, who again left Alessandro Del Piero on the bench and hope to sign Lyon's Fabio Grosso on Monday, had a number of other good chances with Amauri striking a post.
In other games on Sunday, Roberto Donadoni's Napoli beat his former side Livorno 3-1 with new signing Fabio Quagliarella scoring his first two goals for his hometown club.
Fiorentina defeated Palermo 1-0 on a terrible pitch in Florence thanks to Stevan Jovetic's clever flick, while Sampdoria overcame Udinese 3-1, promoted Parma edged past Catania 2-1 and Genoa won 1-0 at Atalanta.
Inter hammered 10-man AC Milan 4-0 in Saturday's derby.
