Third-placed Bayern hammered bottom side St Pauli 8-1 on Saturday, which sealed their hosts relegation, and after Leverkusen drew against Hamburg, Munich are now only three points from second.
Germany striker Mario Gomez netted a hat-trick while Dutch winger Arjen Robben and France star Franck Ribery bagged a brace each as Bayern ran riot at St Pauli's Millerntor stadium.
The win means Bayern can finish no lower than third this season -- confirming their involvement in next season's Champions League.
A win over Stuttgart would see them finish second, as long as Leverkusen lose away to Freiburg next Saturday.
"It would be a sensation if we were to finish second," said Lahm.
"Now the pressure is on Leverkusen.
"We'll do whatever we can to achieve this. We want to beat Stuttgart and bring the season to a decent end at the Allianz Arena.
"Then we'll look and see how Leverkusen get on."
Bayern's caretaker coach Andries Jonker, who will be replaced by Leverkusen's Jupp Heynckes next season, said his side will go full throttle as he prepares for his last game in charge.
"8-1 is unbelievable and astonishing," said the Dutchman.
"I'm looking forward to the game against Stuttgart.
"We'll go full throttle again, and see if we can put pressure on Leverkusen."
Germany striker Gomez, who has now scored 27 league goals in 31 matches this season to make him the league's top-scorer, says the Bavarians have everything still to play for.
"It's good we've hit our minimum target," he said.
"We've had to invest a lot to get there, because this season hasn't gone well for us for long spells.
"So we're even happier about definitely coming third, and maybe even second.
"Let's hope there's still a chance, and we'll give everything until the very last minute.
"I’m assuming I'll finish as top scorer now, but anything can happen in football, so I’ll continue trying to score in the last match."
Having been confirmed as German champions the week before, Borussia Dortmund slumped to a 2-0 defeat at Werder Bremen, but will still be presented with the Bundesliga shield after Saturday's home game against Eintracht Frankfurt.
Their guests are second from bottom and must win in Dortmund to stand any chance of avoiding relegation.
"It was important that we presented ourselves reasonably well here," said Dortmund coach Jurgen Klopp.
"After initial problems, we played quite well."
Klopp said his team will raise their game for the season finale in front of a 80,720-strong crowd.
"We will do everything we can (to win the game), that's what everyone should expect from us," he promised.
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