Schalke have failed to win in one more game than three other teams and only Tasmania Berlin are worse off with 31 matches without victory in the 1965-66.
The hosts opened the scoring thanks to 19-year-old Malick Thiaw. The young centre-back headed his first Bundesliga goal at the far left post after a free-kick from Amine Harit.
But after the break Stuttgart were awarded a penalty after Salif Sane's handball in the box, and Nicolas Gonzalez scored from the spot to equalize.
The visitors had chances to take the three points home, but Tanguy Coulibaly header was cleared by Mark Uth right in front of the goal, while Borna Sosa and Gonzalo Castro efforts were stopped by goalkeeper Frederik Roennow.
A stoppage time finish from Benito Raman almost gave Schalke a first win since Januaty 17 - 2-0 against Borussia Moenchengladbach - but keeper Gregor Kobel avoided it with the tip of his foot.
"It's a dream come true to score in the Bundesliga," Thiaw told streaming portal DAZN. "But would be happier if we had won. I'm a team player, and the team always comes first."
Uth said: "Sadly we couldn't make it, but we played well and must build from that and move forward."
Stuttgart's Marc Oliver Kempf named the outcome "hard" and added: "We should have been brave, we had a good second half. We want to play football and we know what we're capable of."
Schalke remain second last with two points, while Stuttgart move up to 4th. On Saturday champions Bayern Munich travel Cologne, and top of the table RB Leipzig visit Borussia Moenchengladbach.