The home side started strongly and deservedly took the lead after some great work on the left wing by Gervinho.
The former Arsenal man used his pace to get to the byline and cut it across to Maicon, who kept his cool in a crowded area to slot home and make it 1-0.
Daniele De Rossi almost doubled Roma's advantage on 10 minutes, but his free header in the box was kept out by Neto.
Giuseppe Rossi had the away side's first real chance of the game on 22 minutes, bursting into the box before seeing his shot deflected over the bar.
Juan Cuadrado tested the goalkeeper from distance on 37 minutes, but his effort went just wide of the mark.