Following a goalless opening period at the Stadio Olimpico, Mauri slid home Felipe Anderson's low cross to net the opening goal after 51 minutes.
The 34-year-old then steered in a fine second from the edge of the area to double his team's advantage, and Senad Lulic headed in from right-back Dusan Basta's cross to seal the points nine minutes from time.
Lazio will hope to finish the weekend in third, too, as Genoa and Sampdoria - the two teams immediately below them - face clashes with the top two as they meet Roma and Juventus respectively on Sunday.
In Saturday's earlier Serie A match, Andrea Belotti netted an injury time winner to secure a 2-1 win for Palermo over nine-man Sassuolo.
Luca Rigoni handed Palermo an ideal start when he headed home Paulo Dybala's corner after just three minutes.
Sassuolo's task appeared thankless when goalkeeper Andrea Consigli was sent off for a professional foul on Enzo Maresca shortly after the hour, but their ambition was rewarded when Leonardo Pavoletti curled a shot into the top corner five minutes from time.
But Belotti provided a final twist when he beat the offside trap to finish coolly before Pablo Cannavaro was sent off for a kick on Dybala as tempers frayed.
Victory moves Palermo above Sassuolo and into ninth place in the table.
