In form forward Edin Dzeko opened the scoring for Roma 10minutes into the match before Salah doubled the lead seven minutes later.
The Egyptian netted an absolute thunderbolt from the edge of the area as he volleyed a rocket past Joe Hart after an unsuccessfully cleared header to see Roma extend their lead.
This was the 24-year-old’s ninth strike in 18 appearances so far this campaign.
Leandro Paredes than followed with spectacular effort of his own from range to make it 3-0 for the hosts and Belgium international Radja Nainggolan netted his sides fourth courtesy of a brilliant play between Salah and Francesco Totti.
The win was Roma’s fifth successive victory in their last five matches.
This was the second consecutive Serie A match that the Pharaohs midfielder is starting since his return from Afcon. The result sees Giallorossi are currently occupying second spot on the log with 56 points, seven points adrift of leaders Juventus and two above third-placed Napoli.
After missing Thursday’s 4-0 thrashing of Villarreal in the Europa League and it remains to be seen if he will have any part to play in Luciano Spalletti’s side when they host the Spanish side for the return leg at the Stadio Olimpico this coming Thursday.