Eusebio Di Francesco's men played out a thrilling 3-3 draw at Stamford Bridge in Group C two weeks ago but ran away with the return clash to replace the Premier League champions at the top of the standings on Tuesday.
El Shaarawy headed into the match on the back of a spectacular winning goal against Bologna last Saturday and he produced another one for the highlights reel – lashing past Thibaut Courtois first time from 25 yards after 39 seconds.
An error from Antonio Rudiger on his return to Roma allowed El Shaarawy to make it 2-0 and the hosts seldom looked back from that point.
"It's the kind of night that you never forget, for the rest of your life," he told Roma's official website.
"This is a special night – it was my first brace in the Champions League, plus beating Chelsea 3-0 doesn’t happen every day. This win means a lot to us.
"It means a great deal [to go top of the group]. When the draw was made, there was some doubt surrounding us.
"But we went to London and played a really good game, at a tough ground. Now we have an important game before the international break [at Fiorentina in Serie A]. We're purely focused on that."
El Shaarawy's fine run of form over the past week has had the added bonus of prolonging birthday celebrations, after the ex-AC Milan forward turned 25 last Friday.
"Special is the right word," he added. "It was my birthday – it's been an intense week, full of excitement. I'm really happy."