The capital side, who move up to fourth in the table, led 2-0 within 10 minutes thanks to Ciro Immobile's double.
Keita Balde Diao then scored a hat-trick between the 21st and 26th minutes to complete the first-half scoring.
Andrea Rispoli scored twice after the break for Palermo before Luca Crecco's last-minute sixth goal for Lazio.
The only other team to score five goals as quickly in an Italian top-flight match were Juventus, who scored all theirs in 21 minutes in a 5-2 win over Fiorentina 79 years ago.
Match ends, Lazio 6, Palermo 2.
Second Half ends, Lazio 6, Palermo 2.
Goal!  Lazio 6, Palermo 2. Luca Crecco (Lazio) right footed shot from the left side of the six yard box to the centre of the goal following a corner.
Corner,  Lazio. Conceded by Michel Morganella.
Foul by Cristiano Lombardi (Lazio).
Michel Morganella (Palermo) wins a free kick in the defensive half.
Foul by Felipe Anderson (Lazio).
Andrea Rispoli (Palermo) wins a free kick in the defensive half.
Felipe Anderson (Lazio) wins a free kick in the attacking half.
Foul by Bruno Henrique (Palermo).
Substitution, Lazio. Cristiano Lombardi replaces Keita.
Attempt blocked. Giancarlo Gonzalez (Palermo) right footed shot from outside the box is blocked.
Foul by Wallace (Lazio).
Aleksandar Trajkovski (Palermo) wins a free kick in the attacking half.
Foul by Wallace (Lazio).
Ivaylo Chochev (Palermo) wins a free kick in the defensive half.
Wesley Hoedt (Lazio) wins a free kick in the defensive half.
Foul by Ilija Nestorovski (Palermo).
Wesley Hoedt (Lazio) wins a free kick in the attacking half.
Foul by Ilija Nestorovski (Palermo).
Attempt blocked. Lucas Biglia (Lazio) left footed shot from outside the box is blocked.
Attempt blocked. Luca Crecco (Lazio) left footed shot from the left side of the box is blocked. Assisted by Felipe Anderson with a cross.
Substitution, Palermo. Aleksandar Trajkovski replaces Simone Lo Faso.
Offside, Lazio. Stefan de Vrij tries a through ball, but Jordan Lukaku is caught offside.
Attempt missed. Keita (Lazio) right footed shot from outside the box is close, but misses to the left.
Substitution, Lazio. Luca Crecco replaces Sergej Milinkovic-Savic.
Substitution, Palermo. Ivaylo Chochev replaces Mato Jajalo.
Attempt missed. Ciro Immobile (Lazio) left footed shot from the left side of the box is close, but misses to the left. Assisted by Lucas Biglia.
Offside, Lazio. Sergej Milinkovic-Savic tries a through ball, but Wesley Hoedt is caught offside.
Attempt saved. Sergej Milinkovic-Savic (Lazio) right footed shot from outside the box is saved in the bottom right corner.
Alessandro Gazzi (Palermo) is shown the yellow card for a bad foul.
Lucas Biglia (Lazio) wins a free kick in the attacking half.
Foul by Alessandro Gazzi (Palermo).
Attempt blocked. Wesley Hoedt (Lazio) left footed shot from outside the box is blocked.
Ciro Immobile (Lazio) wins a free kick in the attacking half.
Foul by Edoardo Goldaniga (Palermo).
Attempt blocked. Senad Lulic (Lazio) right footed shot from outside the box is blocked. Assisted by Lucas Biglia.
Lucas Biglia (Lazio) wins a free kick in the defensive half.
Foul by Simone Lo Faso (Palermo).
Sergej Milinkovic-Savic (Lazio) is shown the yellow card.
Lazio became the first side to score five goals in the opening 26 minutes of a Serie A match since 1938 as they thrashed struggling Palermo.