During the 2004–05 season, Griazev sustained a back injury and had to withdraw from the 2004 Skate America.[5] He was 7th at 2004 Cup of Russia but then earned silver at Russian Nationals. He went again to the European Championships, where he placed 5th, and moved up a spot at Worlds to 11th.
For the 2005–06 season, Tarasova returned to Russia and so Griazev did as well, training with both Tarasova and Elena Vodorezova in Moscow. Griazev was 9th out of 11 men at the 2005 Skate Canada International. The very next week, however, he won the bronze medal at 2005 Cup of China, his first senior Grand Prix medal. At that competition, he was in the lead after the short program, and earned new personal best scores for his short program, long program, and overall total. At the 2006 Russian nationals, Griazev finished 9th and did not receive a berth to the European Championships and the Olympics. Due to the withdrawal of other skaters, Griazev was sent to 2006 Worlds, where he struggled in the qualifying and short programs, but performed a strong long program. Griazev returned to Russia in March 2006 to take part in the Italian Carnival skating tour produced by Ilia Averbukh. He had also taken part in this tour the previous year. His touring schedule was cut short when he sustained a knee injury and had to undergo surgery.[6]
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.[7]
For the 2007–08 season, Griazev was initially assigned to the 2007 Nebelhorn Trophy competition in Oberdstorf, Germany, but injured ligaments in his ankle in September 2007 and had to withdraw from the event.[6] He won the bronze at the 2007 Cup of Russia in Moscow and placed 7th at the 2007 NHK Trophy. He won the bronze medal at the 2008 Russian Championships.
Griazev placed 5th at the 2009 Russian Championships. He retired from competitive skating following that season. In November 2009, he began skating on cruise ships.[8]