With the win, Roma maintain the six-point gap between them and log leaders Juventus after a thoroughly one-sided contest at Stadio Renato Dall'Ara.
Federico Fazio opened the scoring in the 25th minute following an assist by Konstantinos Manolas before former Chelsea man Salah added the second shortly before the interval.
The Pharaohs international benefited from Edin Dzeko’s clever flick-through as he was played in behind the defence before calmly lobbing the ball over the onrushing goalkeeper from close range.
Salah has now scored 11 goals for Giallorossi in Serie A this campaign and is on the right track to smash the record he achieved last campaign and set a new personal best.
The 24-year-old reached a milestone of 100 goals in midweek with a brace in the 3-2 win over Lazio in the Coppa Italia, and with another strike today, his 102nd, it doesn't seem like he will slow down anytime soon.
Salah left Premier League leaders Chelsea on loan last season in search of regular football and, after impressing with 14 goals in 24 matches, he was retained by Luciano Spalletti on permanent basis and has proved to be an astute addition.
Dzeko rounded off Roma’s rout with a strike in the 75th minute.