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Lazio will face Fiorentina in the quarter finals, which are being played on December 27 and January 3.
Brazilian winger Anderson, who has become one of Lazio's star players since arriving in Italy from Santos in 2013, slotted the home side's 24th-minute second in his second appearance since being sidelined with a knee injury before the start of the season.
Anderson raced through to stroke home Lucas Leiva's fine through ball 13 minutes after Ciro Immobile opened the scoring and his strike was added to by an Agostino Camigliano own goal nine minutes before the break and a smart Immobile chip in the final moments.
Cittadella's cup run came to an end despite a missile of a free-kick from Paolo Bartolomei three minutes before half-time.
