A Nicolo Zaniolo strike and Aleksander Kolarov penalty gave the hosts a comfortable halftime lead but Torino drew level through strikes by Tomas Rincon and Cristian Ansaldi before El Shaarawy secured the points for Roma in the 73rd minute.
The result sees the Rome side move into fourth place on 33 points ahead of the rest of the weekend fixtures, while Torino remain ninth with 27 points after a 12-match unbeaten run on their travels, a record stretching back to April 2018.
"As usual, we made life complicated for ourselves," Roma coach Eusebio Di Francesco told Italian broadcasters.
"Considering the first half performance, we deserved to be more than 2-0 up, but we can't always go at 300 kilometres per hour and must learn to control the game during certain periods.
"It's a lack of experience on our part, but also shows the positives, such as our young players being so eager to keep attacking and creating at all times."
Roma took the lead after 15 minutes thanks to the improvisation of Zaniolo, who managed to gather the rebound from his own attempt while on the ground in a crowded box before pivoting and firing a shot into the roof of the net.
The home side doubled their advantage before the break when Kolarov stroked a penalty into the corner after goalkeeper Salvatore Sirigu brought down El Shaarawy, who has replaced Cengiz Under after six minutes, with a trailing arm.
Torino got back in the game six minutes into the second half when Rincon curled a shot into the bottom corner from just outside the box and the comeback was completed with 22 minutes left on the clock thanks to a superb volley from Ansaldi.
However, Roma rallied and regained the lead six minutes later when El Shaarawy latched onto Lorenzo Pellegrini’s through ball and tucked the finish past Sirigu.
(Reporting by Alasdair Mackenzie; Editing by Ken Ferris and Christian Radnedge)
