[citation needed] In May, Ablyazin was selected, alongside Emin Garibov, David Belyavskiy, Anton Golotsutskov and Aleksandr Balandin to represent Russia at the 2012 European Championships in Montpellier, France.

He was the only Russian male artistic gymnast to win two medals, a bronze on floor and a silver on vault behind Yang Hak-Seon of South Korea, at the 2012 Summer Olympics.

[citation needed] In March, Ablyazin competed at the World Cup, which was held in France, where he won gold on rings and placed second on floor.

[citation needed] In July, Ablyazin, alongside the Russian team (Nikolai Kuksenkov, Emin Garibov, David Belyavskiy and Nikita Ignatyev) competed at the 2013 Summer Universiade in Kazan, Russia, where they won the gold medal, ahead of Ukraine and Japan.

[citation needed] In September, Ablyazin competed at the World Championships in Antwerp, Belgium, but failed to qualify for any event finals.

[citation needed] At the start of the season, Ablyazin competed at the World Cup in Cottbus, Germany and placed first in the rings and floor finals.

In May, he and his teammates (Nikolai Kuksenkov, Aleksandr Balandin, Nikita Ignatyev, David Belyavskiy), competed at the 2014 European Championships in Sofia, Bulgaria.

[citation needed] Ablyazin won a total of four gold medals making him the most successful gymnast in the entire 2014 European Championships.

[citation needed] In October, Ablyazin competed at the 2014 World Championships in Nanning, China and helped the Russian team to a fifth-place finish.

[citation needed] On August 6–16, Ablyazin competed with the Russian Team (together with Ivan Stretovich, Nikita Nagornyy, Nikolai Kuksenkov and David Belyavskiy) at the 2016 Summer Olympics in Rio de Janeiro, he contributed scores of 15.100 in floor, 15.700 in rings, 15.600 vault, helping the Russian men's team win the silver medal with a total of 271.453 points.

[citation needed] On October 2–8, 2017, Ablyazin competed at the 2017 World Championships in Montreal, Canada and finished with only one medal, a silver in the individual still rings event final with a combined score of 15.333 behind the 15.433 posted by the gold medalist Eleftherios Petrounias of Greece.

On September 11, 2021, Ablyazin, together with his gold medal-winning Olympic teammates, was awarded with the Order of Friendship medals by President Vladimir Putin.