* Kiessling on target as Leverkusen beat Stuttgart
* Boateng scores late winner for Schalke
* Hamburg lose fifth game in a row (Recasts, adds quotes, details)
BERLIN, Feb 1 (Reuters) - Hamburg SV, the only ever-present team since the Bundesliga was founded in 1963, dropped into the relegation playoff spot on Saturday after a 3-0 loss at Hoffenheim which left coach Bert van Marwijk fuming.
The Dutchman said his team had played like amateurs after slumping to their fifth defeat in a row to leave them 16th in the 18-team table.
Second-placed Bayer Leverkusen, who had lost their previous three games, revived their campaign by coming from behind to beat VfB Stuttgart 2-1 thanks to Stefan Kiessling's tenth goal of the season and a late winner from Eren Derdiyok.
Kevin-Prince Boateng also scored late to give Schalke 04 a 2-1 win over 10-man VfL Wolfsburg to maintain their challenge for a European place while Augsburg set a club record of seven Bundesliga games without defeat by beating Werder Bremen 3-1.
South Korean pair Park Joo-Ho and Koo Ja-Cheol scored to give Mainz 05 a 2-0 win over Freiburg and Borussia Moenchengladbach dropped out of the top four after losing 3-1 at Hanover 96.
Leverkusen's win made a small dent into Bayern Munich's lead at the top, reducing it to 10 points with the Bavarians still to face Eintracht Frankfurt at home on Sunday.
Unbeaten Bayern have 50 points from 18 games, with Leverkusen on 40, Borussia Dortmund, who won 2-1 at Eintracht Braunschweig on Friday, on 36 and Schalke on 34.
Hoffenheim started the weekend with the worst defensive record in the Bundesliga but handed that over to Hamburg after an embarrassingly easy win.
"Our big problem is that we give away goals too easily," said Van Marwijk, who led the Netherlands to the 2010 World Cup final and took over at Hamburg after Thorsten Fink was sacked early this season. "Their second goal was the crunch point, after that we played like amateurs.
"We must complete a game without conceding a goal if we're not going to score ourselves."
Brazilian forward Roberto Firmino gave Hoffenheim a fourth-minute lead, putting the finishing touch to a swift counter-attack, and Niklas Suele headed the second just before halftime.
Andreas Beck put the finishing touch when he turned in Firmino's pass on the hour, the 44th goal Hamburg have conceded in 19 games.
Leverkusen suffered an early setback when Moritz Leitner gave Stuttgart a 12th minute lead with a 25th metre-shot, the 21-year-old's first-ever Bundesliga goal.
But Kiessling equalised with a typically clinical finish in the 26th minute and Swiss forward Derdiyok won the game with a stooping header six minutes from time.
Schalke took an early lead through Felipe Santana but needed a late goal from Boateng after Maximilian Arnold replied for Wolfsburg, who had Daniel Caligirui sent off for dissent early in the second half.
Augsburg made the worst possible start when Jan-Ingwer Callsen-Bracker headed into his own goal after three minutes but Tobias Werner levelled with a deflected free kick after 11 minutes.
Werder had Santiago Garcia dismissed for a second bookable offence just before halftime and Augsburg took full advantage as Halil Altintop and Andre Hahn wrapped up the three points in the second half, lifting them to ninth. (Reporting by Brian Homewood; editing by Justin Palmer)