It wasn't the internet, which arrived a bit later, but "Samizdat" (?spelling) played a large role. The USSR had decided against the North Korean model of repression and economic (non-)development, and allowed its workers some access to photocopiers, word processors, and other office tools that we take for granted. These were used to propagate publications and opinions which the authorities would have preferred to suppress, but couldn't.
Economics also played a big role. Central planning had failed compared to Western non-centralisation, and citizens of the USSR had gained enough access to the Western world to know that this was the case. Again, interpersonal communications trumped Soviet propaganda from the centre.