Aleksandr Vlasov was selected for the Russian national junior road cycling team in 2014 at the age of 18. He received his first professional contract with Gazprom-RusVelo for the 2018 season. This was followed in 2019 by the title at the Russian road race championships. In the same year, he won a stage at the Tour of Austria. After switching to Astana, Vlasov won two major one-day races in 2020: the Mont Ventoux Challenge and the Giro dell'Emilia. The following year, Vlasov once again became Russian champion, this time in the individual time trial.
In 2022, Vlasov moved to Bora-Hansgrohe and also won his first UCI World Tour race this year at the Tour de Romandie. Other successes include the overall classification and a stage of the Tour of Valencia as well as a stage at the Tour de Suisse.
Aleksandr Vlasov's best finish in a Grand Tour was fourth place in the 2021 Giro d'Italia. In 2022, he finished fifth in the Tour de France. Vlasov finished 11th at the Vuelta a Espana in 2020.