Arjen Robben twice went close and Lewandowski might have got another before Raphael Guerreiro pulled one back to allay Dortmund's fears of a rout.
Bayern go into the Dortmund match looking to bounce back from their first defeat since November in midweek, when they went down 1-0 to Hoffenheim.
The match started in frantic fashion as both sides oozed with attacking flair and Ousmane Dembele produced the first signs of danger for Bayern when he weaved his way past the defence but could only fire wide of Sven Ulreich's goal.
Bayern Munich hosts Borussia Dortmund at the Allianz Arena for a big rivalry game on Saturday.
Ancelotti will hope the Poland worldwide recovers ahead of Wednesday's Champions League tie with Real Madrid as Bayern seek to edge a step closer to European success to add to what will inevitably be another Bundesliga crown. "I just did not want to risk it ahead of Wednesday".
Franck Ribery had given Bayern the lead before Lewandowski made it 2-0 after 10 minutes.
"We're playing a good opponent", Ancelotti said. Bayern Munich will try to rebound from Tuesday's loss to Hoffenheim, while Dortmund is coming off a resounding win over Hamburg.
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Second-placed Leipzig had captain Willi Orban sent off for a second yellow card on 88 minutes for a foul on Leverkusen's Germany forward Kevin Volland.
But despite the numerical disadvantage, Leipzig claimed the three points through their Scandinavian combination.
Ancelotti will not make wholesale changes with the Madrid meeting in mind, despite their 10-point lead at the top of the table, saying: "We need our best performance and our best line-up".
"Now we're in a great position for our next game", he added with RB at home to fifth-placed Freiburg next Saturday.
The game turned out to be a one-sided affair, with Lewandowski taking his league tally to 26 goals in a flawless dress rehearsal before next week's Champions League quarter-final against Real Madrid.
Mainz are only outside the relegation places on goal difference after their 1-0 defeat at Freiburg, whose striker Nils Petersen scored the second-half victor off the bench.
Cologne lost 3-2 at home to local rivals and fellow European hopefuls Borussia Moenchengladbach. Horn conceded two more after halftime, including 'Gladbach captain Lars Stindl's 80th-minute victor.