Kurginjan started at the 2004 Junior World Championships in Beijing on an international level. There he reached at least the quarter-finals over 1500 meters, on the other routes he was eliminated in the heats. Nevertheless, the Russian Federation nominated him for the Short Track World Cup in February 2005 , where he failed to achieve top results in the last two stations of the season. For this he achieved particularly successful results over 1500 meters at the 2005 World Cup and even qualified for the quarter-finals on this long distance, where he failed in fourth. In the 2005/06 World Cup, the Russian took part in all stations and collected several points over the 1500 meter distance, placing him on a good 25th place in the discipline World Cup on this route. At the Junior World Cup in 2006 he even made it to the finals with the relay, but there they were disqualified. Because of his good performance that winter, Kurginjan took part in the 2006 Winter Olympics in Turin as one of only two male short trackers in his country . Besides Mikhail Raschkin he started in all individual races, his best result was a 14th place over 500 meters. In the other competitions he also achieved results close to 15th place.
In the 2006/07 World Cup, Kurginjan achieved two twelfth places as the best results, he did not start at major events. One winter later , he achieved his first top 10 result in the World Cup, a ninth place at the season opener over 1500 meters. In addition, he achieved fourth place in the relay, as well as at the European Championship 2008 , where the Russian also triumphed on the individual routes. First he placed silver over 1500 meters, then fourth in the 1000 meter distance. With these top results he qualified for the 3,000 meter superfinal of the best eight, in which the all-round winner was chosen. Although he did not compete there, he finally achieved sixth place in the all-around result, tied with the German Tyson Heung . He did not defend this previously greatest success of his career at the world championship of the same year in Gangneung , instead he finished 46th and penultimate among 48 participants. In the Short Track World Cup 2008/09 , after four of six stations, a tenth place over 1000 meters is his best result, and he also achieved fourth place with the relay at the first World Cup.
Kurginjan also achieved some national successes, including winning the silver medal over 3000 meters at the Russian Championship in 2005, and in the same year he won the Russian Cup .