Mainz, who had won their first seven games, stayed behind Borussia Dortmund on goal difference. Both teams have 21 points after Borussia won 2-1 at Cologne to go top on Friday.
Much-criticised Bayern Munich striker Mario Gomez scored a hat-trick to give the struggling champions a 3-0 win over Hanover 96 and take them to ninth place on 11 points.
Hamburg's 36-year-old Brazilian midfielder Ze Roberto missed an open goal just before half-time, hitting the post after being set up by Ruud van Nistelrooy who had a goal disallowed for a foul on the hour.
Gomez, who scored 10 goals last season and had not previously hit the target this term, had largely been confined to a substitute's role after becoming the Bundesliga's most expensive signing.
However, he suddenly found his touch and headed in Hamit Altintop's free kick in the 21st minute before adding two more in the last quarter of an hour when he thumped home Toni Kroos's lobbed pass and headed in a Thomas Muller cross.
"When you play for 90 minutes, you always have better chances and possibilities to excel," said Gomez."
In the meeting of the teams who started the day in the bottom two places, Schalke 04, last season's runners-up, were held 2-2 by VfB Stuttgart, who fired coach Christian Gross last week and replaced him with Jens Keller.
Stuttgart twice led through Timo Gebhart and Austrian Martin Harnik while Brazilian Edu grabbed Schalke's first and Dutchman Klaas-Jan Huntelaar rescued a point by converting an 80th-minute penalty.
