For the 2006–07 season, Griazev continued to struggle with consistency, as well as suffering illness at several competitions. At both the 2006 Trophée Eric Bompard and 2006 Cup of Russia, he finished 7th. At the 2007 Russian Championships, Griazev trailed Andrei Lutai after the short program but placed ahead in the long program and won his first national title. He went on to the 2007 European Championships, where he finished 16th and as a result missed the Russian team for the 2007 World Championships. He spent spring 2007 performing with Averbukh's skating tour, which traveled to over twenty cities in Russia, as well as shows in Lithuania, Latvia, and Israel.