(CNN) -- St. Pauli and Kaiserslautern both won on their return to the German Bundesliga on Saturday, while last season's runners-up Schalke and fellow title hopefuls Werder Bremen suffered defeats.
Schalke saw champions Bayern Munich open their account with a 2-1 victory against Wolfsburg on Friday night, but Felix Magath's team went down by the same scoreline at Hamburg as Ruud van Nistelrooy won the battle of former Real Madrid strikers.
Magath threatened to quit the club during the week after being criticized by fans, and his much-heralded new signing Raul made little impact as the veteran Van Nistelrooy grabbed the headlines with both goals to follow up last weekend's German Cup hat-trick.
The Dutchman hit the bar with a fierce free-kick just before halftime and twice put Hamburg ahead to give former Wolfsburg coach Armin Veh a winning start to his tenure, with Schalke reduced to 10 men in the second half when Benedikt Howedes was sent off.
Hamburg, who finished seventh last season, dominated the match and should have scored more goals but did not take the lead until 25 seconds after the halftime break when Van Nistelrooy volleyed in a cross by Eljero Elia.
The 34-year-old then blasted another chance over the bar before Howedes saw red on the hour mark for tripping winger Jonathan Pitroipa, and was then denied by goalkeeper Manuel Neuer.
Jefferson Farfan made Hamburg pay for their profligacy in front of goal when he equalized with an opportunist volley in the 80th minute as he beat his former teammate Heiko Westermann to a free-kick.
But the hosts were not to be denied and Van Nistelrooy buried a typical close-range effort after a surging run down the left by Ze Roberto, who placed a perfect low cross into his path.
St. Pauli scored three goals in the last seven minutes to triumph 3-1 at Freiburg, who had taken the lead on 78 through Papiss Cisse.
The Senegalese striker converted a cross by Congo midfielder Cedrick Makiadi to break the deadlock, but Fabian Boll leveled after Freiberg could not cut out a pass by substitute Richard Sukuta-Pasu, who then made it 2-1 from a tight angle after pouncing on Fin Bartels' deflected shot.
The 20-year-old striker, who is on loan from Bayer Leverkusen, broke on the counter-attack to set up Bartels in time added on to seal the Hamburg-based club's win.
Kaiserslautern also won 3-1, helped by the early sending-off of Cologne's Youssef Mohamad.
The Lebanon defender was red-carded within two minutes -- which by some reports is the fastest in Bundesliga history -- after bringing down Erwin Hoffer.
However, Slovenian striker Milivoje Novakovic put the home side ahead six minutes later after goalkeeper Tobias Sippel dropped a cross before Croatian forward Srdjan Lakic leveled with the first of his two goals with 20 minutes to play.
Lakic made it 2-1 with six minutes left with a deflected shot and substitute Ivo Ilicevic also had some fortune as his shot was diverted into the Cologne net.
Werder Bremen went into the trip to Hoffenheim boosted by the 3-1 Champions League win over Italian club Sampdoria, but ended up losing 4-1 despite taking the lead through an early Torsten Frings penalty.
Hoffenheim bounced back from the third-minute setback, due to handball by Marvin Compper, as they scored all four goals by halftime.
Senegal international striker Demba Ba equalized in the 20th minute when Clemens Fritz could not clear a low cross by Vedad Ibisevic, then he set up Togo-born debutant Peniel Mlapa eight minutes before the break.
Ibisevic made it 3-1 from Luiz Gustavo's pass and Sejad Salihovic sealed it with a fine free-kick.
Hannover, who just avoided relegation last season after the death of Germany goalkeeper Robert Enke, made a positive start to this campaign with a 2-1 win at home to Eintracht Frankfurt.
Konstantin Rausch put Hannover ahead against the run of play in the 21st minute, but Benjamin Kohler leveled from Patrick Ochs' cross before the half-hour.
Ivory Coast striker Didier Ya-Konan scored the winner with 15 minutes left after Frankfurt could not clear Sergio Pinto's free-kick.
Borussia Monchengladbach were held 1-1 at home by Nuremberg, with Jens Hegeler heading the visiting Bavarians ahead before Mohamadou Idrissou equalized in the 31st minute.
In Sunday's matches, Mainz host Stuttgart and then Michael Ballack's Bayer Leverkusen travel to Borussia Dortmund.