Dortmund top scorer Lewandowski tapped in a fine Ivan Perisic cutback 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 keeper 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 Juergen Klopp.
"But we got that third goal and I think overall we are very satisfied."
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 lineup 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.
At the other end of the table