The result made Lazio the favourites to reach the final where they are likely to face Juventus who beat Napoli 3-1 in their opening leg 24 hours earlier.
Serbian midfielder Milinkovic-Savic had already seen one effort saved by Brazilian keeper Alisson before he found the target on the half-hour mark.
Felipe Anderson created the goal, sprinting down the left and past hapless defender Federico Fazio before pulling the ball back for Milinkovic-Savic to score from close range.
Roma almost equalised straightaway but an Edin Dzeko header trimmed the crossbar.
Roma's Egypt international Mohamed Salah also saw a shot hit the post in the second half before Lazio grabbed their second goal in the 78th minute.
This time Senegalese winger Keita Balde was the inspiration, sprinting away from a host of defenders to cross for the unmarked Immobile to sidefoot the ball past the out of position Alisson.