Marco Rose’s men climbed to second in the table after extending their unbeaten run to 16 matches in all competitions.
Two straight draws for Bayern, including against Leipzig, since the restart of the Bundesliga following the winter break have slowed their march towards an 11th successive title.
The Bavarians host fourth-placed Eintracht Frankfurt on Saturday.
Leipzig took the lead in the 25th minute at the Red Bull Arena as Szoboszlai’s powerful 35-yard free-kick bounced past visiting goalkeeper Florian Muller.
The Hungarian winger had previously scored only one league goal this season but he found the net again shortly after half-time.
There was nothing Muller could have done to keep out Szoboszlai’s wonderful volley from the edge of the box.
Stuttgart gave themselves hope of a comeback when Chris Fuhrich scored a penalty midway through the second period.
But Leipzig held on to boost their hopes of a first Bundesliga title and leave Stuttgart mired in relegation trouble, sitting just two points above the bottom two.
AFP
Contact: [email protected]