Martin Jol's Hamburg edged past Zilina in the opening round of UEFA Cup group games while there were fine victories for AC Milan and Sampdoria.
Hamburg matched group F rivals Aston Villa by recording a 2-1 victory over Zilina in Slovakia.
A viral infection forced Mladen Petric out of Sunday's 1-1 draw with Schalke, but the Croatia forward returned to the starting line-up and within 15 minutes had given Hamburg the lead.
Ivica Olic added a second before half-time as Hamburg secured an important win despite substitute Emil Rilke's second-half strike for Zilina.
Milan got their Group E adventure off to the best possible start with a comfortable 3-1 win over Dutch side Heerenveen.
An own goal from Heerenveen midfielder Calvin Jong-a-Pin after 19 minutes set Milan on their way before goals from Gennaro Gattuso and Filippo Inzaghi put the Italians out of sight.
Danijel Pranjic added a late consolation goal for the hosts from the penalty spot.
In Group C, Sampdoria defied their miserable domestic form and recorded a 2-1 victory over Partizan Belgrade in Serbia.
Partizan's Lamine Diarra had cancelled out Emiliano Bonazzoli's opener for Samp, but Daniele Dessena's second-half strike gave the visitors a vital win.
In the other match in the pool, Sevilla began their campaign with a 2-0 win over Stuttgart.
Goals from Romaric and Renato Dirnei in the 15th and 16th minutes were enough to set the 2006 and 2007 champions on their way to the three points.
In Group D, Dinamo Zagreb deservedly edged NEC Nijmegen in a 3-2 thriller.
Mario Mandzukic gave Dinamo the lead after just three minutes, but a Carlos own goal evened things up midway through the first half.
Theo Janssen struck to put NEC ahead with 12 minutes remaining, before goals from substitute Bosko Balaban and Ivica Vrdoljak sealed the points for the Croatian outfit.
In Group H, Nancy and CSKA Moscow posted 3-0 home wins over Feyenoord and Deportivo La Coruna respectively.
Julien Feret and then Monsef Zerka struck inside eight minutes of the restart before Maurilio Helder added a third after 84 minutes for Nancy.
Two goals in the space of three first-half minutes from young midfielder Alan Dzagoev paved the way for CSKA to down Depor, with Vagner Love completing the scoring.
Schalke began Group A with a 3-1 triumph over Paris St Germain.
The hosts took the lead in the 12th minute courtesy of an own goal by PSG defender Larrys Mabiala.
Kevin Kuranyi made it 2-0 after 39 minutes and then set up the third for Halil Altintop 21 minutes from time before Clement Chantome hit a late consolation for the visitors.
Also in the pool, Romano Denneboom scored the only goal as FC Twente clinched an impressive 1-0 home triumph against Racing Santander.
Galatasaray got their Group B campaign off to a winning start with a narrow 1-0 victory over Olympiacos in a closely-contested clash in Istanbul.
Harry Kewell's glancing header was enough to give Michael Skibbe's Turkish champions all three points.
Hertha Berlin fought back to register a hard-earned point in a 1-1 draw against Benfica.
The Portuguese outfit went ahead after 51 minutes through Angel di Maria but Hertha equalised 16 minutes from time through Marko Pantelic.
St Etienne celebrated their return to European action after a 26-year absence by beating FC Copenhagen 3-1 in Group G .
In a dramatic opening, Morten Nordstrand missed a penalty for the hosts just a minute after Bafetimbi Gomis had put St Etienne in front.
Loic Perrin added a second for the visitors in the 37th minute and, though Cesar Santin's penalty reduced the arrears just before the hour, Dimitri Payet's strike sealed the win for the French side.
The other match in the pool saw Rosenborg and Club Brugge battle out a disappointing goalless draw.