Krylov has competed in several national and international chess championships with some notable achievements. In 2004, he tied for the 7-14th position in the World Mind Sports Games. He also appeared in the chess tournament at the 2009 World Mind Sports Games, where he tied for the 6-10th place. In 2014, he tied for the 5-8th position in Moscow Open.
Krylov is also known for his performance in large international chess tournaments. He participated in Aeroflot Open, one of the world's largest open chess tournaments, in 2004, 2005, and 2006, where he achieved a high ranking of 3rd place in 2005.