Dortmund top scorer Lewandowski tapped in a fine Ivan Perisic cut-back in the 22nd minute and Ilkay Gundogan doubled their lead with a curled shot from the edge of the box as the champions extended their unbeaten streak to 23 games with five left to play.
Mario Mandzukic headed in to cut the deficit in the 61st for Wolfsburg, who were left with 10 men a little later after captain Alexander Madlung received a second booking.
Despite frantic efforts by the hosts for an equaliser, Lewandowski killed off the game in a quick break, beating goalkeeper Diego Benaglio in the 90th for his 19th league goal to lift Dortmund to 66 points.
"You have to be happy if you win 3-1 at Wolfsburg who are a very uncomfortable opponent," said Dortmund coach Jurgen Klopp. "But we got that third goal and I think overall we are very satisfied."
Bayern, who are still chasing a treble after qualifying for the Champions League last four, snatched their ninth straight win in all competitions after Bundesliga top scorer Mario Gomez scored twice to take his league tally to 25.
Bayern, who also face Dortmund in the German Cup final in May, were eager go into the April 11 league match-up against Dortmund with only a three-point gap and got off to a flying start.
The hosts, who had midfielder Bastian Schweinsteiger back in the starting line-up after a knee injury, needed only 25 seconds to score. Gomez found the back of the net with a close range effort following a dizzying run down the wing by Franck Ribery straight after the start.
Gomez, in spectacular form this season, added his 25th league goal on the hour, racing into the box to connect with an Arjen Robben pass from the right after Augsburg had briefly levelled with Koo Ja-cheol.
Bayern are second on 63 with five games left in the campaign.
Borussia Monchengladbach lost further ground for automatic Champions League qualification when they drew 0-0 against 17th-placed Hertha Berlin to stay in fourth place on 52.
VfB Stuttgart boosted their chances of European football next season with a 4-1 win over Mainz 05 that lifted them up to fifth place on 43.
At the other end of the table Kaiserslautern dropped deeper into trouble after losing 2-1 at home against Hoffenheim. The basement club seem condemned to go down at the end of the season as they have 20 points, nine below the relegation-playoff threshold, after a 19-match winless streak.
Cologne remain third from bottom, in the relegation play-off spot, following a 1-1 draw against Werder Bremen, who are now without a win for four games. Werder are sixth with 41 points and in danger of dropping out of the European spots.
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