Alexander Baschenow made his international debut as part of the FIS Cup on December 12, 2013 in Notodden . As seventh, he jumped straight into the top ten. After two fifth places in Râşnov, Romania, in February 2014, he traveled with the Russian B-team to the Ski Jumping Continental Cup (COC) in Falun . He made his debut in this series on March 1st, 2014 with a 49th place on the normal hill. On March 14th he collected his first four points with rank 27 in Nizhny Tagil , with which he reached rank 170 in the overall ranking of the Continental Cup. From September 2014 Basschenow was again used in the FIS Cup, where he found it difficult to match the previous year's performance. Despite poor points, he started again in the Continental Cup in January 2015. In Sapporo , Japan , he again jumped into the points in the first of three competitions. At the following Nordic Junior World Ski Championships in 2015 in Almaty , he jumped to 35th place in the individual, before finishing 11th with the team in the team competition. In Nizhny Tagil, Baschenow collected COC points again at the end of the season. In the same place he finally made his debut in the ski jumping World Cup on December 11, 2015 , but remained without points in both competitions. As a result, he stayed in the Continental Cup, but could not celebrate any further successes. In January he took part in the qualification for the World Cup in Sapporo, but failed at the age of 45 before the competition.
On September 10, 2016 Baschenow made his debut in the Ski Jumping Grand Prix , but did not reach the second round in Tchaikovsky as 44th. For the winter of 2016/17 Baschenow received another starting place in the B-team. In the third competition in Vikersund he was able to win COC points again. At the beginning of February Baschenow started at the Winter Universiade 2017 in Almaty. After a tenth place in the individual competition, he won the gold medal in the team competition together with Roman Trofimow and Mikhail Maximotschkin . As a result, he again took part in the World Cup qualifications in Sapporo and Pyeongchang . However, he only managed to jump into the competition in Pyeongchang, where he was eliminated again without points after round one. At Raw Air 2017 , which was held for the first time in March , he finished 65th overall by participating in the team competitions. In the individual competitions, he consistently missed the qualification. In ski flying in Vikersund, he also failed to make it into the competition. Only with the team did he reach rank 11 in team flying.