In April 2012, Tkachenko said that they would spend some time preparing for the following season in Marina Zueva and Igor Shpilband's group in the United States, however, the coaches parted ways so the skaters decided to train with Shpilband in Novi, Michigan. At a camp in Bulgaria, Tkachenko lost his balance while practicing a lift on the floor in skates and stepped on Riazanova's hand; she had surgery on her hand and recovered well. At the suggestion of Tatiana Tarasova, they decided to scrap a new free dance to Pink Floyd's Hey You and made a new one to a waltz from the Godfather films. Riazanova/Tkachenko won bronze medals at the 2012 Skate Canada and 2012 Trophée Eric Bompard. They repeated as bronze medalists at the 2013 Russian Championships.