Cologne and RB Leipzig remained unbeaten after drawing 1-1 in a match which started 15 minutes late because the home fans staged a sit-down protest in the street to prevent the visitors' team bus from reaching the stadium.
Schalke took an early lead but their players were left speechless after a mistake by midfielder Nabil Bentaleb set up Lukas Rupp's 40th minute winner for Hoffenheim, who themselves had drawn their opening four matches.
"We have actively helped to make it 2-1 from 1-0 ahead," said coach Markus Weinzierl, appointed in June in place of Andre Breitenreiter who left after failing to earn qualification for the Champions League last season.
"I don't know where the problem lies," said goalkeeper Ralf Faehrmann. "We are in a situation where words fail me. Things aren't working up front and we make the simplest mistakes at the back. It's getting more difficult week by week."
Schalke, the only Bundesliga team without a point after five games, got the perfect start when Breel Embolo raced past two defenders and crossed for Eric Maxim Choupo-Moting to head in after four minutes.
But Schalke, who have not finished outside the top six since 2010-11, handed the initiative back to the hosts, who levelled with a powerful header by Andrej Kramaric in the 17th minute.
Klaas-Jan Huntelaar headed against the post for Schalke but Hoffenheim went ahead five minutes before the break.
Kerem Demirbay pounced on a poor Bentaleb pass, burst forward and laid the ball off for Rupp to slide in at the far post. Hoffenheim, who are ninth on seven points, dominated the second half as the Royal Blues went down with barely a whimper.
In Cologne, Leipzig's bus eventually reached the stadium via an alternative route after the latest protest against energy drinks manufacturer Red Bull's ownership of the club.
Rival fans say Leipzig, who have risen from the fifth tier since being founded in 2009, are an example of a 'plastic club' without a genuine fan base which owes its existence to financial support from wealthy backers who give it an unfair advantage.
Leipzig's Oliver Burke became the first Scotsman to score in the Bundesliga since Brian O'Neil in 1999 when his fourth minute goal gave the visitors the lead.
Japanese Yuya Osako lashed the ball home from a tight angle to level before halftime, leaving Cologne third with 11 points behind leaders Bayern Munich (15) and Borussia Dortmund (12).
(Writing by Brian Homewood, editing by Pritha Sarkar and Ken Ferris)
