Lewandowski netted the opener after just nine minutes before Corentin Tolisso doubled Bayern’s lead prior to the interval.
Poland international Lewandowski then scored his second after the hour mark and completed his treble with 16 minutes remaining.
The second-half strikes took Lewandowski to 300 Bundesliga goals as he became the first player to reach the landmark since Gerd Muller in 1976.
Bayern also eclipsed their own record by scoring for the 66th consecutive league match. The win restores Bayern’s advantage over second-placed Borussia Dortmund following their 5-1 win against Freiburg on Friday evening.
Robert Andrich and Patrik Schick struck in the second half as Bayer Leverkusen moved up to third with a 2-1 win at Borussia Monchengladbach.
Nico Elvedi netted for the hosts in the closing stages but Leverkusen held their nerve to secure a first triumph in five league outings.
Elsewhere in Germany’s top flight, Hoffenheim suffered a 2-1 defeat to Union Berlin, while RB Leipzig recorded a 2-0 win over Stuttgart.
Wolfsburg and Hertha Berlin played out a goalless draw, with Mainz increasing their unbeaten streak to seven matches following a 1-0 win over Bochum.
In Serie A, Juventus secured a routine 2-0 win at home to Udinese.
Paulo Dybala, a reported Tottenham target, scored after 19 minutes before Weston McKennie sealed the three points with 11 minutes remaining.
Juventus are fifth in the table, eight points behind leaders Inter Milan having played two more matches.
Ciro Immobile scored a brace as Lazio ran out 3-0 winners against bottom side Salernitana, with Torino coming from a goal down to win 2-1 at Sampdoria.
Paris St Germain extended their Ligue 1 lead over Nice to 11 points following a 2-0 home triumph against Brest.
Kylian Mbappe opened the scoring with a fine finish after 32 minutes before Thilo Kehrer sealed the victory in the second half.
In the day’s other fixture, Seko Fofana netted in stoppage time as Lens edged a 2-1 win at St Etienne.