Playing their fifth game in 15 days and four days after their 5-1 Champions League demolition of Arsenal, Bayern never hit top form but are cruising to a record-extending fifth straight league crown with second-placed RB Leipzig losing 1-0 to VfL Wolfsburg.
Unusually, Bayern had to strike against the run of play with Eintracht coming close on two occasions before Poland forward Lewandowski put them ahead after good work from Thomas Mueller in the 38th minute.
Brazilian Douglas Costa doubled their lead three minutes later, finishing off a quick break and Lewandowski perfectly converted a sweet cross from Arjen Robben 10 minutes after the restart for his 20th league goal of the season.
The Bavarians, whose defender Jerome Boateng returned from injury after more than three months out, are now on 59 points.
Leipzig are second on 49 after Mario Gomez grabbed the winner for the visitors with his eighth goal of the season as the Wolves celebrated their first win under coach Andries Jonker in his second game in charge.
The win lifted Wolfsburg three points away from the relegation zone and into 14th.
Borussia Dortmund could not take advantage of Leipzig's rare slip-up, losing 2-1 at Hertha Berlin, who went ahead with Salomon Kalou's sixth league goal in the 11th minute.
Dortmund came agonisingly close to an equaliser through Pierre-Emerick Aubameyang right after the restart.
But the Bundesliga's top scorer, who hit a hat-trick in their 4-0 win over Benfica in the Champions League in midweek, did not miss in the 55th, drilling in from a tight angle to level with his 22nd league goal.
Marvin Plattenhardt dashed Dortmund's hopes, however, thundering a 71st-minute free kick into the top corner to leave Dortmund stuck on 43 points in third place and Hertha closing in on 40 in fifth.
Hoffenheim missed the chance to leapfrog into third after a 1-1 draw at Freiburg and remained fourth on 42.
(Reporting by Karolos Grohmann, editing by Ed Osmond/Rex Gowar)
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