Radja Nainggolan and Edin Dzeko's strikes secured the three points for Luciano Spalleti's men as they reclaimed second spot on the Serie A log.
After featuring in all six of the Pharaohs' matches at the continental spectacle in Gabon – where he was also named as one of the tournament's outstanding players – Salah returned to Roma’s starting lineup.
He featured for the whole game as Egypt ceded a 1-0 lead to lose 2-1 to Cameroon in last Sunday’s final, but showed no signs of ‘post Afcon hangover’ and was his usual best as he architected both of the Giallorossi’s goals.
The attacker first won his side a 17th-minute penalty when he was fouled inside the area but Dzeko dragged his effort wide.
He returned again minutes later but turned a free header over from a few yards out as he led Roma's quest for the opener.
The deadlock was eventually broken when Kevin Strootman and Salah combined for Nainggolan, who collected the North African''s pass before turning and lashing a low shot beyond Alex Cordaz in the hosts’ goals.
Despite the penalty miss, Dzeko did get his goal eventually, as Salah raced on to a through ball from Leandro Paredes and pulled back from the by-line for the former Manchester City man to tap in relatively uninterrupted.
The 24-year old was later withdrawn for Daniele De Rossi.