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. Ablyazin contributed scores of 15.833 on floor, 15.500 on rings, 15.366 on vault toward Russia's first-place finish with a total score of 267.959, ahead of Great Britain. Individually, Ablyazin placed first in all events he qualified, winning the gold medal on floor with a score of 15.700, on rings, scoring 15.800 (tied with teammate Aleksandr Balandin) and on vault with a total score of 15.150.