The victory has thus ended Germany's upset history in the European tournament that they have not yet won a single match after they claimed the title in 1996.
"Winning the first game is very important, that add our confidence," said Loew after the match.
For Poland, their dream of beating Germany awaits next occasion.
After Sunday's matches, both Germany and Croatia boast three points but Germany edged out the latter with one more goal to take the first place in Group B.
Austria and Poland are listed third and fourth due to lost goal difference.
Poland's Ebi Smolarek fights for the ball against Germany's Christoph Metzelder (top) during their Group B Euro 2008 soccer match at the Woerthersee Stadium in Klagenfurt, June 8, 2008.
Poland's Jacek Bak challenges Germany's Clemens Fritz (R) during their Group B Euro 2008 soccer match at the Woerthersee Stadium in Klagenfurt, June 8, 2008.
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