The Bosnian hitman bagged a brace, with Stephan El Shaarawy and Daniele De Rossi scoring once apiece, and Mario Pasalic scored the consolation goal for the hosts.
Salah and Dzeko got the scoring underway early on when they combined for the seventh occasion so far this season, the most that any one player in the division has set up another.
The assist was Salah's tenth of the campaign, as he became the only Roma player to hit double figures for goals and assists this term.
The 24-year-old’s impressive displays through the month of April have also seen him announced as the club's player of the month for April according to the Roma website.
Salah enjoyed an impressive goalscoring spree in April, as he managed to hit the back of the net five times, including a brace in a 4-1 win against Pescara.
He also scored another double against arch-rivals Lazio in a 3-2 victory in the Coppa Italia semi-finals, although the Giallorossi were knocked out on aggregate as they were defeated 2-0 in the first-leg at the Stadio Olimpico.