Mirko Vucinic latched on to a pass from deep by Daniele De Rossi before slotting the ball into the corner and Philippe Mexes headed home in the first half to put the hosts in command of the tie.
The victory stretched Roma's unbeaten run in all competitions to 18 games, having moved level on points with second-placed AC Milan in Serie A on Sunday with a 2-1 win over Siena.
On Thursday, striker Vucinic, gave them a 12th-minute lead with the help of some distracted defending.
French defender Mexes beat their back-line to a David Pizarro free-kick to extend and seal Roma's win in the 40th. Serie A leaders Inter Milan beat Fiorentina 1-0 at the San Siro on Wednesday in the first leg of the other semifinal.
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