Spiridonova made her international debut at the 2012 Pre-Olympic Youth Cup in Bergisch-Gladbach, Germany, where she won the all-around gold medal.
2013 was Spiridonova's breakout year. She took gold with her team and silver on uneven bars at the Russian Junior Championships in the spring. She competed at the Olympic Hopes, winning gold with her team and on uneven bars, bronze in the all-around, and placing fifth on vault. She went on to compete at the KSI Cup, winning team and all-around gold medals.
Spiridonova's senior debut came at the 2014 Cottbus World Cup, but she did not make the event finals. She then competed at the Russian Championships in April, winning gold on bars, silver with her team and on balance beam, and placing fifth in the all-around, and seventh on floor.
At the 2014 European Championships, Spiridonova competed on uneven bars, balance beam and floor exercise. She scored 14.900 on uneven bars which qualified her to the event finals in 4th place. She also scored a 14.058 on beam and 11.900 on floor after a fall. In the team final, Spiridonova contributed scores of 15.066 on bars, 12.300 on beam and 13.100 on floor towards the Russian team's bronze medal finish.
Individually, she won the bronze medal in the uneven bars final with a score of 15.283. On 29 October she placed first ahead of Larisa Iordache at the Arthur Gander Memorial, her first international win at the senior level. Days later, she partnered up with male Russian gymnast Nikita Ignatyev to win her second international title at the Swiss cup. At the Massila Master, she claimed the first all-around crown of her career.
Spiridonova competed at the 2015 Russian Championships in Penza, Russia on 2–8 March 2015. She won a silver medal with her team, as well as placing 4th in the all around, winning gold on the uneven bars, and silver on the balance beam.
Due to her strong performance, Spiridonova was selected to compete at the 2015 European Championships in Montpellier, France on 15–19 April. She placed 13th in the all around final after complications on beam and floor, and she won the gold medal on the uneven bars, beating out the reigning European UB champion, Becky Downie, by 0.2.
At the 2015 World Gymnastics Championships in Glasgow, Spiridonova became a World Champion on the uneven bars, together with three other gymnasts who were part of a four-way tie.
Spiridonova competed at the 2016 Russian Artistic Gymnastics Championships in Penza, Russia from 28 March-10 April 2016. She won a silver medal with her team and tied for gold on the uneven bars with Daria Skrypnik. At the conclusion of the National Championships, Spiridonova, along with Aliya Mustafina, Angelina Melnikova, Seda Tutkhalyan, and Ksenia Afanasyeva, was selected to compete for Russia at the 2016 European Championships in Bern, Switzerland on 1-5 June. She helped Russia qualify in 2nd place with a score of 173.261 and finished in 4th on the uneven bars with a score of 14.733. Despite the 2-per-country rule, she did replace teammate Melnikova in the uneven bars final because of her strength on the event. In the Team Final, she contributed to a 15.333 on uneven bars to lead Russia to a first place finish with an overall score of 175.212. She won the silver medal on the uneven bars, losing to the 2014 UB Champion, Great Britain's Becky Downie by 0.034. Her teammate Mustafina won the bronze.
At the 2016 Russian Cup, Spridonova finished 4th with her team and won bronze on the uneven bars. At the conclusion of the Russian Cup, Spiridonova, along with Mustafina, Tutkhalyan, Melnikova, and Maria Paseka, was selected to represent Russia at the 2016 Summer Olympics in Rio de Janeiro, Brazil. In the midst of the Team Russia Doping Scandal, both the men's and women's gymnastics teams were cleared to compete days before the Games began.
At the 2016 Olympic Games, Spiridonova helped Russia qualify into the Team Finals in 3rd place with an overall score of 174.620. She also qualified into the Uneven Bars final in 4th place with a score of 15.683 along with Mustafina. Spiridonova also finished in a tie for 19th on balance beam with a score of 14.266 and tied for 73rd on floor exercise with a score of 12.033. In the Team Final, she contributed to a 15.100 on uneven bars to lead Russia to a silver medal with an overall score of 176.688. In the Individual Uneven Bars Final, she fell on one of her transition skills and finished in 8th place with a score of 13.966.