Schwaab turned the ball into his own goal in the 42nd minute and Leverkusen subsequently defended their lead stoutly to claim the victory.
Leverkusen coach Sami Hyypia named an unchanged side to the one that defeated Freiburg 3-1 a week ago while for Stuttgart, the loss of the injured Serdar Tasci saw Schwaab moved into the centre of the defence and Cristian Molinaro start at left full-back.
Their task was to keep last season's top goalscorer Stefan Kiessling quiet, yet he had two decent opportunities in the opening three minutes.
Fortunately for the Stuttgart rearguard, goalkeeper Sven Ulreich was on hand both times to prevent Kiessling from scoring his third goal in as many games this season, including the first round of the DFB-Pokal.
Stuttgart did not give the impression of being the home side as Leverkusen took the game to them, Ulreich again coming to the hosts' rescue before Sidney Sam hit the post.
A goal was looming and it arrived three minutes before half-time with Schwaab inadvertently turning Sebastian Boenisch's low cross into his own goal at the near post.
Cacau was sent on by Labbadia at the start of the second half as Stuttgart had to chase the game.
There was more verve about their play, but like in Mainz a week ago, they were unable to put the ball in the back of the net.
The closest they came was in the 82nd minute when Christian Gentner's shot flew wide and the end of the game was greeted by a chorus of whistles from the fans.