In a whirlwind first-half performance top scorer Lewandowski struck twice and James Rodriguez, Thomas Mueller and Franck Ribery were also on target for the Bavarians, who face Sevilla in the Champions League last eight next week.
"The team was outstanding over 90 minutes and in the first half it was a gala performance," Bayern coach Juppp Heynckes told reporters.
"We made the best of our superiority in our game and skills. We went out to win this game because we want to lay down a marker."
Lewandowski, who confirmed his fine form with his third goal of the afternoon in the 88th minute to put the seal on a one-sided game, had also put them ahead after five minutes as Bayern scored virtually at will.
Before Dortmund's defence had any time to recover Bayern scored twice more, through Rodriguez and Mueller, to deflate opponents who are battling for a Champions League spot.
Lewandowski and Ribery scored within minutes of each other to complete their first-half demolition before they eased off after the break.
Bayern moved to 69 points, 17 ahead of second-placed Schalke 04 with six matches remaining. Dortmund who lost for the first time in the league under coach Peter Stoeger, remained third on 48.
"We are bitterly disappointed," said Stoeger. "We offered far too little resistance. Bayern took advantage of every mistake we made. We are at the moment a long way away from Bayern Munich."
But Heynckes' side will have to wait a little longer to clinch the title.
Earlier on Saturday, Schalke beat 10-man Freiburg 2-0 to delay Bayern's title celebrations.
RB Leipzig worked their way back into Champions League contention with a nervous 3-2 victory at Hanover 96 that lifted them to 46 points and fourth place, a point ahead of Bayer Leverkusen, who managed only a goalless draw against Augsburg.
The top four teams qualify automatically for the Champions League group stage next season.
(Reporting by Karolos Grohmann,; Editing by Ed Osmond, Neville Dalton)
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