Leipzig stayed second in the table after their captain Sabitzer opened the scoring with less than a minute gone with a powerful drive.
Germany striker Timo Werner, defender Marcel Halstenberg, new signing Angelino and Emil Forsberg hit second-half goals as Leipzig built on their 1-0 midweek Champions League win at Tottenham.
It was another impressive away display, especially as their flight home following the Spurs game was delayed in the early hours of Thursday.
“We didn’t expect it to be so easy after our tough Champions League match,” admitted Sabitzer.
“But we did very well from the first minute. We’re going to be tough to stop playing like that.”
Leipzig kept pace with Bayern who squeezed past bottom side Paderborn on Friday.
Sabitzer gave Leipzig a spectacular lead by smashing a long-range shot past goalkeeper Alexander Nuebel.
An hour later, Werner claimed his 21st league goal of the season by rifling into the top corner past Nuebel, who will join Bayern for next season.
It turned into a rout when Halstenberg headed in Leipzig’s third goal on 68 minutes, then Angelino, on loan from Manchester City, beat two defenders for their fourth on 81 minutes.
In the dying stages, Leipzig winger Christopher Nkunku produced his fourth assist to tee up Forsberg, on for Werner, to slot home.
– Haaland strikes again –
Earlier, Erling Braut Haaland scored his 40th goal of the season in Borussia Dortmund’s 2-0 win at Werder Bremen.
The 19-year-old has netted 12 times in eight games since joining Dortmund for 20 million euros ($22 million) in December.
Haaland, who scored twice in Tuesday’s Champions League last 16, first-leg win over Paris Saint-Germain, also scored 28 goals for Salzburg this term.
Dortmund ground out a victory which left them third after showing some early nerves in Bremen where they crashed to a 3-2 German Cup defeat earlier this month.
“We allowed them almost nothing and controlled the game more in the second half,” said Dortmund midfielder Emre Can.
“Then Bremen got tired and we scored our goals at the right time.”
Centre-back Dan-Axel Zagadou gave the visitors the lead by volleying home a Jadon Sancho corner on 52 minutes.
