The Polish striker opened the scoring with a penalty in the first half and sealed the win in the second after a Bayern corner.
"We knew it wouldn't be easy but we've taken a good step forward," said Lewandowski, who was already looking ahead to Saturday's game at Bundesliga leader Borussia Dortmund. "We had the game in control for the decisive moments. So a win is good for confidence."
The home side had struggled to create any chances of note until Serbian defender Uros Cosic was penalized for pulling Lewandowski back before the half-hour mark, and Lewandowski scored from the spot.
Bayern dominated possession and Lewandowski grabbed his fourth Champions League goal of the season after a corner from Joshua Kimmich with just under 20 minutes remaining.
With 10 points from four games, Bayern is top of Group E.
"We deserved to win, I'm satisfied with the result," said Bayern coach Niko Kovac, who is under pressure after a series of lackluster results. "There were no fireworks, but we have 10 points, it looks good."
Ajax, which drew at Benfica 1-1 in the other group game on Wednesday, is second on eight points with two games remaining, followed by Benfica on four. AEK is last after four defeats.