Fiorentina, who beat Roma by the same score in a Serie A match last month when Luis Enrique's side had three players sent off, had the better of the first half.
However, the hosts went ahead in the 53rd minute when Francesco Totti's pass set 19-year-old Lamela through to score with a shot between goalkeeper Neto's legs.
Totti also set up the former River Plate player's second goal 14 minutes later and a poor clearance by Neto allowed Fabio Borini to complete the scoring.
Chievo sprang a surprise in Wednesday's other tie, winning 2-1 at Udinese, who are third in Serie A and unbeaten at home, with a stoppage-time goal from Cyril Thereau.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.