Now with nine games to go, Bayern are slight favorites, while the Black and Yellows are now the hunters, and being in that role is much more suited to them.
"We are where we wanted to be, at the top of the table, and we want to stay there".
Lewandowski is also now the Bundesliga's top goalscorer having netted 17 league goals so far this season and gave a positive response when asked whether he could end his career with Bayern.
Third placed Leipzig played out a goalless stalemate with Augsburg, and Borussia Monchengladbach returned to winning ways after beating Mainz 1-0. "Stuttgart had parked a huge bus in front of their goal", Dortmund coach Lucien Favre said of only their second win in the last six league games.
A nervous-looking Marco Reus dispatched the penalty.
In Dortmund, late goals by Paco Alcacer and Chelsea-bound Christian Pulisic saw off dogged Stuttgart, but Borussia are now second after 23 weeks on top.
Pulisic added gloss to the result with a third in stoppage time, but it was not enough to keep BVB top of the pile.
Borussia Dortmund's best form came in the first half of the season when they were playing their natural football, without any expectations or pressure of being in a title race.
Thomas Mueller, Mats Hummels, and Jerome Boateng all started for Bayern, days after being dropped by Germany coach Joachim Loew. "We must accept that, even if it hurts".
A throughball from James found Gnabry and he unselfishly squared for Lewandowski to tap in and pass veteran former Bayern forward Claudio Pizarro on the list of foreign goalscorers. Goals from Joshua Kimmich and Lewandowski completed their rout. The side turns attention to Liverpool's visit in the Champions League on Wednesday.