Imrie tried a curling shot from outside the box 15 minutes from time as Hamilton sought a grandstand finish, but his effort was easily held by Esson atthe top-left corner.
With first-choice penalty takers Adrian Mutu and Stevan Jovetic both injured, Vargas took responsibility to score his first goal of the season atthe Stadio Artemio Franchi, placing his penalty into the top left-hand corner of the goal.
The ever-threatening Boral fired a shot at Lehmann in the 71st minute before former Hitzlsperger saw his left-footed effort go just wide of the top corner.