Lazio, who were held to a disappointing 0-0 draw in Limassol in the previous clash, started the stronger in Rome and came close through Floccari and Balde Keita in the opening exchanges.
It was the attacking duo who combined to break the deadlock on 14 minutes, as Keita jinxed his was through a series of challenges before squaring for Floccari to finish from close range.
Lazio continued to pile on the pressure and Floccari had his second from a Keita cross shortly before the break, as the Italian headed home the 18-year-old's corner for his fourth in this season's competition.
However, the visitors stunned Stadio Olimpico just two minutes later, as Papoulis struck a fierce effort from the edge of the area past Etrit Berisha.
Lazio controlled the majority of the second half without being able to kind a killer third goal, and Papoulis almost made them pay in the final 20 minutes as he latched on to a hopeful long ball, but Berisha smartly denied him.
Apollon continued to threaten in the closing stages but Lazio held on for a vital three points, moving them four clear of the Cypriots in Group J with just two games to play.