Crawford clocked 19.79sec ahead of Bernard Williams (20.01sec) with Justin Gatlin, the 100m winner, taking the bronze in 20.03sec.
Crawford was diplomatic afterwards. He said: "I didn't let the booing affect me. I think I understood what they were going through. We are here at the birthplace of the Olympics and the defending champion is from Greece and he was not allowed to compete.
"I can understand that they were upset but I don't know why they had to react like this."