The Romans, who scored 25 goals in their previous 11 home games, tried to make an early breakthrough at the Stadio Olimpico as first Senad Lulic fired over the bar before Felipe Anderson was denied by keeper Nicola Leali.
On 66 minutes, Frosinone almost edged in front when Leonardo Blanchard's header struck the crossbar.
However, Lazio finally took the lead with 10 minutes left as Balde Diao's shot from Djordjevic's cross found the bottom corner of the net.
The hosts sealed victory in the fourth minute of stoppage time as Djordjevic netted the Biancocelesti's second of the evening.
The result sees Lazio move into the top three in Serie A, with Inter Milan and Fiorentina ahead of the Eagles.