According to this article in Frankfurter Allgemeine Zeitung from 2006 the average GDR citizen was not allowed to attend games during the World Cup in West Germany. Instead fans were handpicked when "worthy and reliable". According to the article "hundreds of Stasi agents [...] dressed as football fans" were brought to the stadium in Hamburg with two trains to show support for the GDR.

East Germany won 1-0 against West Germany

Edit: Low-res screenshot of GDR fans celebrating Jürgen Sparwasser's winning goal