Schalke avoided a record-equalling 31st consecutive Bundesliga game without a victory on Saturday as American teenager Matthew Hoppe netted a hat-trick in a 4-0 thrashing of Hoffenheim to lift his side off the bottom of the table.
"I was able to take my chances," Hoppe said modestly after becoming the first American to score a Bundesliga hat-trick.
"The win will give us confidence and some momentum. There are 19 games left, hopefully we can stay up in the first division."
After enduring a 30-match winless run in the league, the Royal Blues enjoyed their first Bundesliga win in just under a year as 19-year-old Hoppe converted three chances created by Morocco's Amine Harit, who scored the fourth goal.
After getting a win in only his second game in charge, Schalke coach Christian Gross praised Hoppe and the "outstanding" display of goalkeeper Ralf Faehrmann.
"We have to build on the result. There are still a lot of difficult games to come," Gross added with Bayern Munich, who crushed Schalke 8-0 on the opening day of the season, visiting in a fortnight.
Mainz replace Schalke at the bottom of the table after a 2-0 home defeat to Eintracht Frankfurt.
Tasmania Berlin, who went 31 games without a victory in the 1965/66 season, keep the Bundesliga record for the longest winless run.
After league leaders Bayern Munich crashed to a 3-2 defeat at Borussia Moenchengladbach on Friday, second-placed RB Leipzig can go top with a home win against Borussia Dortmund later on Saturday.
In Gelsenkirchen, Hoffenheim were missing 11 players either injured or suspended, while the hosts were captained by Sead Kolasinac who was making his first Schalke appearance back on loan from Arsenal.
"The white shorts of all my teammates were filthy dirty - that is what we need, what we all want to see," Kolasinac said in praising his team's workrate.
Hoppe broke the deadlock with a deft chip just before the break, then doubled the lead on 57 minutes when Harit's pass again put him in behind the defence to calmly round Hoffenheim's goalkeeper and fire into an empty net.
The American claimed his hat-trick just after the hour mark when put into space by another sublime Harit pass to fire home with another deft chip.
Harit then completed the rout by hitting the bottom left-hand corner ten minutes from time.
- Leverkusen stumble again -
After defeats to Bayern and Eintracht Frankfurt, third-placed Bayer Leverkusen drew 1-1 at home to Werder Bremen as Patrik Schick equalised after Omer Toprak put Bremen ahead from a free-kick with only their second chance of the game.
Union Berlin climbed to fourth after a controversial 2-2 draw at home to Wolfsburg, who came from behind after Maximilian Arnold was sent off just after the break.
Renato Steffen gave Wolfsburg an early lead with a header, but Union striker Sheraldo Becker equalised with a crisp shot after squandering a clear chance.
It was 1-1 at the break, but Arnold was shown a straight red for a nudge on Liverpool loanee Taiwo Awoniyi just outside the area and Union midfielder Robert Andrich fired in the resulting free-kick on 52 minutes.
Union had the ball in the net again with an hour played, but the goal was disallowed as the referee judged Awoniyi had fouled Wolfsburg goalkeeper Koen Casteels.
Wolfsburg striker Wout Weghorst equalised on 67 minutes by converting a penalty after a handball by Union defender Marcus Ingvartsen.
Freiburg set a new club record of five straight league wins, which has seen them climb from 14th to eighth in the table, with a 5-0 romp at home to Cologne.