Simone Padoin scored the only goal of the game in the 72nd minute as Juve clinched their 31st victory of the season - a record in Italy's top flight. The Turin club had sealed their 30th scudetto without kicking a ball on Sunday when Roma lost 4-1 against Catania.
The unofficial celebrations took place 24 hours earlier when Juve players staged an impromptu party in the team's hotel that lasted into the early hours of the morning.
Juve, who have now won all of their 18 games at home, held on to continue their bid to break the 100-point barrier in Serie A. They have 96 points with two games remaining.
Hellas looked to have secured all three points when substitute Romulo gave them a 3-2 lead with seven minutes remaining. Lazio, who had Senad Lulic sent off for a straight red soon after, drew level when Mauri tapped in his own missed penalty.
Keita had scored the first goal of the game for Lazio on the half-hour mark but Hellas striker Marquinho equalised seven minutes later. Lulic put the home side back in front after one hour of play only for Juan Manuel Iturbe to make it 2-2 nine minutes later.
The outcome at the Stadio Olimpico has left both sides in the top half of the standings, level on 53 points. They are two points adrift of Torino, who are sixth and hold the last UEFA Europa League qualifying spot with two games remaining.